@article{RosenblumPikovskij2015, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Two types of quasiperiodic partial synchrony in oscillator ensembles}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {1}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.012919}, pages = {8}, year = {2015}, abstract = {We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.}, language = {en} } @article{KumarRosenblum2021, author = {Kumar, Mohit and Rosenblum, Michael}, title = {Two mechanisms of remote synchronization in a chain of Stuart-Landau oscillators}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {104}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {5}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.104.054202}, pages = {6}, year = {2021}, abstract = {Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of remote synchrony in a small network of three coupled Stuart-Landau oscillators using recent results on higher-order phase reduction. We analytically demonstrate the role of two factors promoting remote synchrony. These factors are the nonisochronicity of oscillators and the coupling terms appearing in the secondorder phase approximation. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths.}, language = {en} } @article{PerezVelazquezErraRosenblum2015, author = {Perez-Velazquez, Jose Luis and Erra, Ramon Guevara and Rosenblum, Michael}, title = {The Epileptic Thalamocortical Network is a Macroscopic Self-Sustained Oscillator: Evidence from Frequency-Locking Experiments in Rat Brains}, series = {Scientific reports}, volume = {5}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/srep08423}, pages = {7}, year = {2015}, abstract = {The rhythmic activity observed in nervous systems, in particular in epilepsies and Parkinson's disease, has often been hypothesized to originate from a macroscopic self-sustained neural oscillator. However, this assumption has not been tested experimentally. Here we support this viewpoint with in vivo experiments in a rodent model of absence seizures, by demonstrating frequency locking to external periodic stimuli and finding the characteristic Arnold tongue. This result has important consequences for developing methods for the control of brain activity, such as seizure cancellation.}, language = {en} } @article{ScheffczykKrampeEngbertetal.1997, author = {Scheffczyk, Christian and Krampe, Ralf-Thomas and Engbert, Ralf and Rosenblum, Michael and Kurths, J{\"u}rgen and Kliegl, Reinhold}, title = {Tempo-induced transitions in polyrhythmic hand movements}, year = {1997}, abstract = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.}, language = {en} } @article{MontaseriYazdanpanahPikovskijetal.2013, author = {Montaseri, Ghazal and Yazdanpanah, Mohammad Javad and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Synchrony suppression in ensembles of coupled oscillators via adaptive vanishing feedback}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {23}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {3}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4817393}, pages = {12}, year = {2013}, abstract = {Synchronization and emergence of a collective mode is a general phenomenon, frequently observed in ensembles of coupled self-sustained oscillators of various natures. In several circumstances, in particular in cases of neurological pathologies, this state of the active medium is undesirable. Destruction of this state by a specially designed stimulation is a challenge of high clinical relevance. Typically, the precise effect of an external action on the ensemble is unknown, since the microscopic description of the oscillators and their interactions are not available. We show that, desynchronization in case of a large degree of uncertainty about important features of the system is nevertheless possible; it can be achieved by virtue of a feedback loop with an additional adaptation of parameters. The adaptation also ensures desynchronization of ensembles with non-stationary, time-varying parameters. We perform the stability analysis of the feedback-controlled system and demonstrate efficient destruction of synchrony for several models, including those of spiking and bursting neurons.}, language = {en} } @article{RosenblumAbelKurthsetal.1999, author = {Rosenblum, Michael and Abel, Hans-Henning and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten}, title = {Synchronization in the human cardiorespiratory system}, year = {1999}, language = {en} } @article{RosenblumKurthsPikovskijetal.1998, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij and Schafer, C. and Tass, Peter and Abel, Hans-Henning}, title = {Synchronization in Noisy Systems and Cardiorespiratory Interaction}, year = {1998}, language = {en} } @article{RosenblumPikovskijKurths2004, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Synchronization approach to analysis of biological systems}, issn = {0219-4775}, year = {2004}, abstract = {In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach}, language = {en} } @book{BlechmanLandaRosenblum1995, author = {Blechman, Ilja I. and Landa, Polina S. and Rosenblum, Michael}, title = {Synchronization and chaotization in interacting dynamical systems}, series = {Preprint NLD}, volume = {24}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {40 S.}, year = {1995}, language = {en} } @book{PikovskijRosenblumKurths2001, author = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {Synchronization : a universal concept in nonlinear sciences}, series = {Cambridge nonlinear science series}, volume = {12}, journal = {Cambridge nonlinear science series}, edition = {1st paperback ed., repr}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, isbn = {0-521-59285-2}, pages = {XIX, 411 S. : Ill., graph. Darst.}, year = {2001}, language = {en} } @article{TeichmannRosenblum2019, author = {Teichmann, Erik and Rosenblum, Michael}, title = {Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {29}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {9}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5118843}, pages = {11}, year = {2019}, abstract = {We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.}, language = {en} } @article{MaistrenkoPenkovskyRosenblum2014, author = {Maistrenko, Yuri and Penkovsky, Bogdan and Rosenblum, Michael}, title = {Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {89}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {6}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.89.060901}, pages = {5}, year = {2014}, abstract = {We discuss the desynchronization transition in networks of globally coupled identical oscillators with attractive and repulsive interactions. We show that, if attractive and repulsive groups act in antiphase or close to that, a solitary state emerges with a single repulsive oscillator split up from the others fully synchronized. With further increase of the repulsing strength, the synchronized cluster becomes fuzzy and the dynamics is given by a variety of stationary states with zero common forcing. Intriguingly, solitary states represent the natural link between coherence and incoherence. The phenomenon is described analytically for phase oscillators with sine coupling and demonstrated numerically for more general amplitude models.}, language = {en} } @article{PikovskijRosenblum2009, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Self-organized partially synchronous dynamics in populations of nonlinearly coupled oscillators}, issn = {0167-2789}, doi = {10.1016/j.physd.2008.08.018}, year = {2009}, abstract = {We analyze a minimal model of a population of identical oscillators with a nonlinear coupling-a generalization of the popular Kuramoto model. In addition to well-known for the Kuramoto model regimes of full synchrony, full asynchrony, and integrable neutral quasiperiodic states, ensembles of nonlinearly coupled oscillators demonstrate two novel nontrivial types of partially synchronized dynamics: self-organized bunch states and self-organized quasiperiodic dynamics. The analysis based on the Watanabe-Strogatz ansatz allows us to describe the self-organized bunch states in any finite ensemble as a set of equilibria, and the self-organized quasiperiodicity as a two-frequency quasiperiodic regime. An analytic solution in the thermodynamic limit of infinitely many oscillators is also discussed.}, language = {en} } @article{BordyugovPikovskijRosenblum2010, author = {Bordyugov, Grigory and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Self-emerging and turbulent chimeras in oscillator chains}, issn = {1539-3755}, doi = {10.1103/Physreve.82.035205}, year = {2010}, abstract = {We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e., a state with coexisting regions of complete and partial synchrony, emerges via a supercritical bifurcation from a homogeneous state. We develop a theory of chimera based on the Ott-Antonsen equations for the local complex order parameter. Applying a numerical linear stability analysis, we also describe the instability of the chimera and transition to phase turbulence with persistent patches of synchrony.}, language = {en} } @article{RosenblumPengIvanovetal.1998, author = {Rosenblum, Michael and Peng, C. K. and Ivanov, Plamen Ch. and Mietus, J. and Havlin, Shlomo and Stanley, H. Eugene and Goldberger, Ary L.}, title = {Scaling and universality in heart rate variability distributions}, year = {1998}, language = {en} } @article{KrylovDylovRosenblum2020, author = {Krylov, Dmitrii and Dylov, Dmitry V. and Rosenblum, Michael}, title = {Reinforcement learning for suppression of collective activity in oscillatory ensembles}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {30}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {3}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5128909}, pages = {10}, year = {2020}, abstract = {We present the use of modern machine learning approaches to suppress self-sustained collective oscillations typically signaled by ensembles of degenerative neurons in the brain. The proposed hybrid model relies on two major components: an environment of oscillators and a policy-based reinforcement learning block. We report a model-agnostic synchrony control based on proximal policy optimization and two artificial neural networks in an Actor-Critic configuration. A class of physically meaningful reward functions enabling the suppression of collective oscillatory mode is proposed. The synchrony suppression is demonstrated for two models of neuronal populations-for the ensembles of globally coupled limit-cycle Bonhoeffer-van der Pol oscillators and for the bursting Hindmarsh-Rose neurons using rectangular and charge-balanced stimuli.}, language = {en} } @article{BlahaPikovskijRosenblumetal.2011, author = {Blaha, Karen A. and Pikovskij, Arkadij and Rosenblum, Michael and Clark, Matthew T. and Rusin, Craig G. and Hudson, John L.}, title = {Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {84}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.84.046201}, pages = {7}, year = {2011}, abstract = {Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.}, language = {en} } @article{KralemannPikovskijRosenblum2011, author = {Kralemann, Bj{\"o}rn and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Reconstructing phase dynamics of oscillator networks}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {21}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {2}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.3597647}, pages = {10}, year = {2011}, abstract = {We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.}, language = {en} } @misc{CestnikRosenblum2017, author = {Cestnik, Rok and Rosenblum, Michael}, title = {Reconstructing networks of pulse-coupled oscillators from spike trains}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {760}, issn = {1866-8372}, doi = {10.25932/publishup-43628}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436285}, pages = {8}, year = {2017}, abstract = {We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections.}, language = {en} } @article{CestnikRosenblum2017, author = {Cestnik, Rok and Rosenblum, Michael}, title = {Reconstructing networks of pulse-coupled oscillators from spike trains}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {96}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.96.012209}, pages = {3455 -- 3461}, year = {2017}, abstract = {We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections.}, language = {en} } @article{KralemannPikovskijRosenblum2014, author = {Kralemann, Bjoern and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Reconstructing effective phase connectivity of oscillator networks from observations}, series = {New journal of physics : the open-access journal for physics}, volume = {16}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/16/8/085013}, pages = {21}, year = {2014}, abstract = {We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.}, language = {en} } @article{KralemannPikovskijRosenblum2014, author = {Kralemann, Bjoern and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Reconstructing connectivity of oscillator networks from multimodal observations}, series = {Biomedizinische Technik = Biomedical engineering}, volume = {59}, journal = {Biomedizinische Technik = Biomedical engineering}, publisher = {De Gruyter}, address = {Berlin}, issn = {0013-5585}, doi = {10.1515/bmt-2014-4089}, pages = {S220 -- S220}, year = {2014}, language = {en} } @misc{RosenblumPikovskijKuehnetal.2021, author = {Rosenblum, Michael and Pikovskij, Arkadij and K{\"u}hn, Andrea A. and Busch, Johannes Leon}, title = {Real-time estimation of phase and amplitude with application to neural data}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {1866-8372}, doi = {10.25932/publishup-54963}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-549630}, pages = {11}, year = {2021}, abstract = {Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal's past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient's beta-band brain activity.}, language = {en} } @article{RosenblumPikovskijKuehnetal.2021, author = {Rosenblum, Michael and Pikovskij, Arkadij and K{\"u}hn, Andrea A. and Busch, Johannes Leon}, title = {Real-time estimation of phase and amplitude with application to neural data}, series = {Scientific reports}, volume = {11}, journal = {Scientific reports}, publisher = {Springer Nature}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-021-97560-5}, pages = {11}, year = {2021}, abstract = {Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal's past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient's beta-band brain activity.}, language = {en} } @article{MrowkaPatzakRosenblum2000, author = {Mrowka, Ralf and Patzak, Andreas and Rosenblum, Michael}, title = {Qantitative analysis of cardiorespiratory synchronization in infants}, issn = {0218-1274}, year = {2000}, language = {en} } @article{PopovychLysyanskyRosenblumetal.2017, author = {Popovych, Oleksandr V. and Lysyansky, Borys and Rosenblum, Michael and Pikovskij, Arkadij and Tass, Peter A.}, title = {Pulsatile desynchronizing delayed feedback for closed-loop deep brain stimulation}, series = {PLoS one}, volume = {12}, journal = {PLoS one}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0173363}, pages = {29}, year = {2017}, abstract = {High-frequency (HF) deep brain stimulation (DBS) is the gold standard for the treatment of medically refractory movement disorders like Parkinson's disease, essential tremor, and dystonia, with a significant potential for application to other neurological diseases. The standard setup of HF DBS utilizes an open-loop stimulation protocol, where a permanent HF electrical pulse train is administered to the brain target areas irrespectively of the ongoing neuronal dynamics. Recent experimental and clinical studies demonstrate that a closed-loop, adaptive DBS might be superior to the open-loop setup. We here combine the notion of the adaptive high-frequency stimulation approach, that aims at delivering stimulation adapted to the extent of appropriately detected biomarkers, with specifically desynchronizing stimulation protocols. To this end, we extend the delayed feedback stimulation methods, which are intrinsically closed-loop techniques and specifically designed to desynchronize abnormal neuronal synchronization, to pulsatile electrical brain stimulation. We show that permanent pulsatile high-frequency stimulation subjected to an amplitude modulation by linear or nonlinear delayed feedback methods can effectively and robustly desynchronize a STN-GPe network of model neurons and suggest this approach for desynchronizing closed-loop DBS.}, language = {en} } @article{PikovskijRosenblumZaksetal.1999, author = {Pikovskij, Arkadij and Rosenblum, Michael and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Phase synchronization of regular and chaotic oscillators}, year = {1999}, language = {en} } @phdthesis{Rosenblum2003, author = {Rosenblum, Michael}, title = {Phase synchronization of chaotic systems : from theory to experimental applications}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000682}, school = {Universit{\"a}t Potsdam}, year = {2003}, abstract = {In einem klassischen Kontext bedeutet Synchronisierung die Anpassung der Rhythmen von selbst-erregten periodischen Oszillatoren aufgrund ihrer schwachen Wechselwirkung. Der Begriff der Synchronisierung geht auf den ber{\"u}hmten niederl{\"a}andischen Wissenschaftler Christiaan Huygens im 17. Jahrhundert zur{\"u}ck, der {\"u}ber seine Beobachtungen mit Pendeluhren berichtete. Wenn zwei solche Uhren auf der selben Unterlage plaziert wurden, schwangen ihre Pendel in perfekter {\"U}bereinstimmung. Mathematisch bedeutet das, daß infolge der Kopplung, die Uhren mit gleichen Frequenzen und engverwandten Phasen zu oszillieren begannen. Als wahrscheinlich {\"a}ltester beobachteter nichtlinearer Effekt wurde die Synchronisierung erst nach den Arbeiten von E. V. Appleton und B. Van der Pol gegen 1920 verstanden, die die Synchronisierung in Triodengeneratoren systematisch untersucht haben. Seitdem wurde die Theorie gut entwickelt, und hat viele Anwendungen gefunden. Heutzutage weiss man, dass bestimmte, sogar ziemlich einfache, Systeme, ein chaotisches Verhalten aus{\"u}ben k{\"o}nnen. Dies bedeutet, dass ihre Rhythmen unregelm{\"a}ßig sind und nicht durch nur eine einzige Frequenz charakterisiert werden k{\"o}nnen. Wie in der Habilitationsarbeit gezeigt wurde, kann man jedoch den Begriff der Phase und damit auch der Synchronisierung auf chaotische Systeme ausweiten. Wegen ihrer sehr schwachen Wechselwirkung treten Beziehungen zwischen den Phasen und den gemittelten Frequenzen auf und f{\"u}hren damit zur {\"U}bereinstimmung der immer noch unregelm{\"a}ßigen Rhythmen. Dieser Effekt, sogenannter Phasensynchronisierung, konnte sp{\"a}ter in Laborexperimenten anderer wissenschaftlicher Gruppen best{\"a}tigt werden. Das Verst{\"a}ndnis der Synchronisierung unregelm{\"a}ßiger Oszillatoren erlaubte es uns, wichtige Probleme der Datenanalyse zu untersuchen. Ein Hauptbeispiel ist das Problem der Identifikation schwacher Wechselwirkungen zwischen Systemen, die nur eine passive Messung erlauben. Diese Situation trifft h{\"a}ufig in lebenden Systemen auf, wo Synchronisierungsph{\"a}nomene auf jedem Niveau erscheinen - auf der Ebene von Zellen bis hin zu makroskopischen physiologischen Systemen; in normalen Zust{\"a}nden und auch in Zust{\"a}nden ernster Pathologie. Mit unseren Methoden konnten wir eine Anpassung in den Rhythmen von Herz-Kreislauf und Atmungssystem in Menschen feststellen, wobei der Grad ihrer Interaktion mit der Reifung zunimmt. Weiterhin haben wir unsere Algorithmen benutzt, um die Gehirnaktivit{\"a}t von an Parkinson Erkrankten zu analysieren. Die Ergebnisse dieser Kollaboration mit Neurowissenschaftlern zeigen, dass sich verschiedene Gehirnbereiche genau vor Beginn des pathologischen Zitterns synchronisieren. Außerdem gelang es uns, die f{\"u}r das Zittern verantwortliche Gehirnregion zu lokalisieren.}, language = {en} } @article{RosenblumOsipovPikovskijetal.1997, author = {Rosenblum, Michael and Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillators by external driving}, year = {1997}, language = {en} } @article{ZaksRosenblumPikovskijetal.1997, author = {Zaks, Michael A. and Rosenblum, Michael and Pikovskij, Arkadij and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillations in terms of periodic orbits}, issn = {1054-1500}, year = {1997}, language = {en} } @article{PikovskijRosenblumKurths2000, author = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {Phase synchronization in regular and chaotic systems}, issn = {0218-1274}, year = {2000}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization in noisy and chaotic oscillators}, year = {1997}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization in driven and coupled chaotic oscillators}, year = {1997}, language = {en} } @article{PikovskijRosenblumOsipovetal.1997, author = {Pikovskij, Arkadij and Rosenblum, Michael and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization effects in a lattice of nonidentical R{\"o}ssler oscillators}, year = {1997}, language = {en} } @article{BaibolatovRosenblumZhanabaevetal.2009, author = {Baibolatov, Yernur and Rosenblum, Michael and Zhanabaev, Zeinulla Zh. and Kyzgarina, Meyramgul and Pikovskij, Arkadij}, title = {Periodically forced ensemble of nonlinearly coupled oscillators : from partial to full synchrony}, issn = {1539-3755}, doi = {10.1103/PhysRevE.80.046211}, year = {2009}, abstract = {We analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling. Without forcing, the system exhibits complicated collective dynamics, even for the simplest case of identical phase oscillators: due to nonlinearity, the synchronous state becomes unstable for certain values of the coupling parameter, and the system settles at the border between synchrony and asynchrony, what can be denoted as partial synchrony. We find that an external common forcing can result in two synchronous states: (i) a weak forcing entrains only the mean field, whereas the individual oscillators remain unlocked to the force and, correspondingly, to the mean field; (ii) a strong forcing fully synchronizes the system, making the phases of all oscillators identical. Analytical results are confirmed by numerics.}, language = {en} } @article{MauRosenblum2022, author = {Mau, Erik Thomas Klaus and Rosenblum, Michael}, title = {Optimizing charge-balanced pulse stimulation for desynchronization}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {32}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {1}, publisher = {AIP}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/5.0070036}, pages = {15}, year = {2022}, abstract = {Collective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it is undesirable, which calls for control techniques. In this paper, we focus on pulsatile control, with the goal to either increase or decrease the level of synchrony. We quantify this level by the entropy of the phase distribution. Motivated by possible applications in neuroscience, we consider pulses of a realistic shape. Exploiting the noisy Kuramoto-Winfree model, we search for the optimal pulse profile and the optimal stimulation phase. For this purpose, we derive an expression for the change of the phase distribution entropy due to the stimulus. We relate this change to the properties of individual units characterized by generally different natural frequencies and phase response curves and the population's state. We verify the general result by analyzing a two-frequency population model and demonstrating a good agreement of the theory and numerical simulations.}, language = {en} } @article{SchwabedalPikovskijKralemannetal.2012, author = {Schwabedal, Justus T. C. and Pikovskij, Arkadij and Kralemann, Bj{\"o}rn and Rosenblum, Michael}, title = {Optimal phase description of chaotic oscillators}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {85}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.85.026216}, pages = {9}, year = {2012}, abstract = {We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincare surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rossler and Lorenz systems.}, language = {en} } @article{ZaikinRosenblumLandaetal.1998, author = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen}, title = {On-off itermittency phenomena in a pendulum with a randomly vibrating suspension axis}, year = {1998}, language = {en} } @article{RosenblumPikovskij2019, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Numerical phase reduction beyond the first order approximation}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {29}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {1}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5079617}, pages = {6}, year = {2019}, abstract = {We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss the limitations of the approach. Published under license by AIP Publishing.}, language = {en} } @article{RosenblumPikovskij2019, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Nonlinear phase coupling functions: a numerical study}, series = {Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, volume = {377}, journal = {Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, number = {2160}, publisher = {Royal Society}, address = {London}, issn = {1364-503X}, doi = {10.1098/rsta.2019.0093}, pages = {12}, year = {2019}, abstract = {Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here, we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we determine and numerically analyse the coupling functions up to the fourth order in the force strength. We show that the found nonlinear phase coupling functions can be used for predicting synchronization regions of the forced oscillator.}, language = {en} } @article{ScheffczykEngbertKrampeetal.1996, author = {Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen and Rosenblum, Michael and Zaikin, Alexei A.}, title = {Nonlinear Modelling of Polyrhythmic Hand Movements}, year = {1996}, language = {en} } @misc{ErraVelazquezRosenblum2017, author = {Erra, Ramon Guevara and Velazquez, Jose L. Perez and Rosenblum, Michael}, title = {Neural Synchronization from the Perspective of Non-linear Dynamics}, series = {Frontiers in computational neuroscience / Frontiers Research Foundation}, volume = {11}, journal = {Frontiers in computational neuroscience / Frontiers Research Foundation}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1662-5188}, doi = {10.3389/fncom.2017.00098}, pages = {4}, year = {2017}, language = {en} } @article{AmaralGoldbergerHavlinetal.1999, author = {Amaral, Luis A. Nunes and Goldberger, Ary L. and Havlin, Shlomo and Rosenblum, Michael and Struzik, Zbigniew R. and Stanley, H. Eugene and Ivanov, Plamen Ch.}, title = {Multifractality in human heartbeat dynamics}, year = {1999}, language = {en} } @article{MoellerKittelKruegeretal.2008, author = {M{\"o}ller, Sebastian and Kittel, Ren{\´e} and Kr{\"u}ger, Tom and Srunk, Soeren and Rosenblum, Michael and Wick, Ditmar}, title = {Movement profiles of the balance breaking (Kuzushi) of top judoka}, isbn = {978-3-8322-8390-2}, year = {2008}, language = {en} } @article{MoellerKittelKruegeretal.2009, author = {M{\"o}ller, Sebastian and Kittel, Ren{\´e} and Kr{\"u}ger, Tom and Sprunk, S{\"o}ren and Wick, Ditmar and Rosenblum, Michael}, title = {Movement profiles of the balance breaking (Kuzushi) of top judoka}, isbn = {978-3-8322-8390-2}, year = {2009}, language = {en} } @article{ZaikinRosenblumScheffczyketal.1997, author = {Zaikin, Alexei A. and Rosenblum, Michael and Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen}, title = {Modeling qualitative changes in bimanual movements}, year = {1997}, language = {en} } @article{RosenblumPikovskijKurthsetal.2002, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen and Osipov, Grigory V. and Kiss, Istvan Z. and Hudson, J. L.}, title = {Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics}, year = {2002}, language = {en} } @book{RosenblumSchaeferAbeletal.1997, author = {Rosenblum, Michael and Sch{\"a}fer, Carsten and Abel, Hans-Henning and Kurths, J{\"u}rgen}, title = {Interrelationship of Parasympathetic Innervation of the Sinoatrial Node and the Atrioventricular Node of Human Heart}, issn = {1120-1797}, year = {1997}, language = {en} } @misc{PimenovaGoldobinRosenblumetal.2016, author = {Pimenova, Anastasiya V. and Goldobin, Denis S. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Interplay of coupling and common noise at the transition to synchrony in oscillator populations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103471}, pages = {7}, year = {2016}, abstract = {There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.}, language = {en} } @article{PimenovaGoldobinRosenblumetal.2016, author = {Pimenova, Anastasiya V. and Goldobin, Denis S. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Interplay of coupling and common noise at the transition to synchrony in oscillator populations}, series = {Scientific reports}, volume = {6}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/srep38518}, pages = {7}, year = {2016}, abstract = {There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.}, language = {en} } @article{CestnikRosenblum2018, author = {Cestnik, Rok and Rosenblum, Michael}, title = {Inferring the phase response curve from observation of a continuously perturbed oscillator}, series = {Scientific reports}, volume = {8}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-018-32069-y}, pages = {10}, year = {2018}, abstract = {Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and application of a specifically designed input. However, isolation is not always feasible and we are compelled to observe the system in its natural environment under free-running conditions. To that end we propose an approach relying only on passive observations of the system and its input. We illustrate it with simulation results of an oscillator driven by a stochastic force.}, language = {en} } @article{CestnikRosenblum2018, author = {Cestnik, Rok and Rosenblum, Michael}, title = {Inferring the phase response curve from observation of a continuously perturbed oscillator}, series = {Scientific Reports}, volume = {8}, journal = {Scientific Reports}, publisher = {Nature Publishing Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-018-32069-y}, pages = {1 -- 10}, year = {2018}, abstract = {Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and application of a specifically designed input. However, isolation is not always feasible and we are compelled to observe the system in its natural environment under free-running conditions. To that end we propose an approach relying only on passive observations of the system and its input. We illustrate it with simulation results of an oscillator driven by a stochastic force.}, language = {en} } @misc{CestnikRosenblum2018, author = {Cestnik, Rok and Rosenblum, Michael}, title = {Inferring the phase response curve from observation of a continuously perturbed oscillator}, series = {Scientific Reports}, journal = {Scientific Reports}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-418425}, pages = {10}, year = {2018}, abstract = {Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and application of a specifically designed input. However, isolation is not always feasible and we are compelled to observe the system in its natural environment under free-running conditions. To that end we propose an approach relying only on passive observations of the system and its input. We illustrate it with simulation results of an oscillator driven by a stochastic force.}, language = {en} } @article{KralemannFruehwirthPikovskijetal.2013, author = {Kralemann, Bjoern and Fruehwirth, Matthias and Pikovskij, Arkadij and Rosenblum, Michael and Kenner, Thomas and Schaefer, Jochen and Moser, Maximilian}, title = {In vivo cardiac phase response curve elucidates human respiratory heart rate variability}, series = {Nature Communications}, volume = {4}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/ncomms3418}, pages = {9}, year = {2013}, abstract = {Recovering interaction of endogenous rhythms from observations is challenging, especially if a mathematical model explaining the behaviour of the system is unknown. The decisive information for successful reconstruction of the dynamics is the sensitivity of an oscillator to external influences, which is quantified by its phase response curve. Here we present a technique that allows the extraction of the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators-in this case heartbeat and respiration-in its natural environment and under free-running conditions. We use this method to obtain the phase-coupling functions describing cardiorespiratory interactions and the phase response curve of 17 healthy humans. We show for the first time the phase at which the cardiac beat is susceptible to respiratory drive and extract the respiratory-related component of heart rate variability. This non-invasive method for the determination of phase response curves of coupled oscillators may find application in many scientific disciplines.}, language = {en} } @article{RosenblumBezerianosPatzaketal.2002, author = {Rosenblum, Michael and Bezerianos, Anastassios and Patzak, Andreas and Mrowka, Ralf}, title = {Identification of coupling direction : Application to cardiorespiratory interaction}, year = {2002}, language = {en} } @article{PollatosYeldesbayPikovskijetal.2014, author = {Pollatos, Olga and Yeldesbay, Azamat and Pikovskij, Arkadij and Rosenblum, Michael}, title = {How much time has passed? Ask your heart}, series = {Frontiers in neurorobotics}, volume = {8}, journal = {Frontiers in neurorobotics}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1662-5218}, doi = {10.3389/fnbot.2014.00015}, pages = {1 -- 9}, year = {2014}, abstract = {Internal signals like one's heartbeats are centrally processed via specific pathways and both their neural representations as well as their conscious perception (interoception) provide key information for many cognitive processes. Recent empirical findings propose that neural processes in the insular cortex, which are related to bodily signals, might constitute a neurophysiological mechanism for the encoding of duration. Nevertheless, the exact nature of such a proposed relationship remains unclear. We aimed to address this question by searching for the effects of cardiac rhythm on time perception by the use of a duration reproduction paradigm. Time intervals used were of 0.5, 2, 3, 7, 10, 14, 25, and 40s length. In a framework of synchronization hypothesis, measures of phase locking between the cardiac cycle and start/stop signals of the reproduction task were calculated to quantify this relationship. The main result is that marginally significant synchronization indices (Sls) between the heart cycle and the time reproduction responses for the time intervals of 2, 3, 10, 14, and 25s length were obtained, while results were not significant for durations of 0.5, 7, and 40s length. On the single participant level, several subjects exhibited some synchrony between the heart cycle and the time reproduction responses, most pronounced for the time interval of 25s (8 out of 23 participants for 20\% quantile). Better time reproduction accuracy was not related with larger degree of phase locking, but with greater vagal control of the heart. A higher interoceptive sensitivity (IS) was associated with a higher synchronization index (SI) for the 2s time interval only. We conclude that information obtained from the cardiac cycle is relevant for the encoding and reproduction of time in the time span of 2-25s. Sympathovagal tone as well as interoceptive processes mediate the accuracy of time estimation.}, language = {en} } @article{RosenblumKurthsSchaeferetal.1998, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten and Abel, Hans-Henning}, title = {Heartbeat synchronized with ventilation}, year = {1998}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {From Phase to Lag Synchronization in Coupled Chaotic Oscillators}, year = {1997}, abstract = {We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.}, language = {en} } @article{EhrichPikovskijRosenblum2013, author = {Ehrich, Sebastian and Pikovskij, Arkadij and Rosenblum, Michael}, title = {From complete to modulated synchrony in networks of identical Hindmarsh-Rose neurons}, series = {European physical journal special topics}, volume = {222}, journal = {European physical journal special topics}, number = {10}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2013-02025-8}, pages = {2407 -- 2416}, year = {2013}, abstract = {In most cases tendency to synchrony in networks of oscillatory units increases with the coupling strength. Using the popular Hindmarsh-Rose neuronal model, we demonstrate that even for identical neurons and simple coupling the dynamics can be more complicated. Our numerical analysis for globally coupled systems and oscillator lattices reveals a new scenario of synchrony breaking with the increase of coupling, resulting in a quasiperiodic, modulated synchronous state.}, language = {en} } @article{IvanovNuenesAmaralGoldbergeretal.2001, author = {Ivanov, Plamen Ch. and Nuenes Amaral, Lu{\´i}s A. and Goldberger, Ary L. and Havlin, Shlomo and Rosenblum, Michael and Stanley, H. Eugene and Struzik, Zbigniew R.}, title = {From 1/f noise to multifractal cascades in heartbeat dynamics}, issn = {1054-1500}, year = {2001}, language = {en} } @article{TemirbayevZhanabaevTarasovetal.2012, author = {Temirbayev, Amirkhan A. and Zhanabaev, Zeinulla Zh. and Tarasov, Stanislav B. and Ponomarenko, Vladimir I. and Rosenblum, Michael}, title = {Experiments on oscillator ensembles with global nonlinear coupling}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {85}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {1}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.85.015204}, pages = {4}, year = {2012}, abstract = {We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett. 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.}, language = {en} } @article{CimponeriuRosenblumPikovskij2004, author = {Cimponeriu, Laura and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Estimation of delay in coupling from time series}, issn = {1063-651X}, year = {2004}, abstract = {We demonstrate that a tune delay in weak coupling between two self-sustained oscillators can be estimated from the observed time series data. We present two methods which are. based on the analysis of interrelations between the phases of the signals. We show analytically and numerically that irregularity of the phase dynamics (due to the intrinsic noise or chaos) is essential for determination,of the delay. We compare and contrast both methods to the standard cross-correlation analysis}, language = {en} } @article{PolitiRosenblum2015, author = {Politi, Antonio and Rosenblum, Michael}, title = {Equivalence of phase-oscillator and integrate-and-fire models}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {91}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.91.042916}, pages = {11}, year = {2015}, abstract = {A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization is rather general and can be observed for arbitrarily small coupling strength in any model class. As a byproduct of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with delta pulses and a suitable phase response curve.}, language = {en} } @article{RosenblumPikovskij2018, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Efficient determination of synchronization domains from observations of asynchronous dynamics}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {10}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5037012}, pages = {8}, year = {2018}, abstract = {We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized. Published by AIP Publishing.}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Effect of phase synchronization in driven chaotic oscillators}, year = {1997}, language = {en} } @article{VlasovRosenblumPikovskij2016, author = {Vlasov, Vladimir and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {49}, journal = {Journal of physics : A, Mathematical and theoretical}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/49/31/31LT02}, pages = {8}, year = {2016}, abstract = {As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.}, language = {en} } @article{PikovskijRosenblum2011, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Dynamics of heterogeneous oscillator ensembles in terms of collective variables}, series = {Physica :D, Nonlinear phenomena}, volume = {240}, journal = {Physica :D, Nonlinear phenomena}, number = {9-10}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2011.01.002}, pages = {872 -- 881}, year = {2011}, abstract = {We consider general heterogeneous ensembles of phase oscillators, sine coupled to arbitrary external fields. Starting with the infinitely large ensembles, we extend the Watanabe-Strogatz theory, valid for identical oscillators, to cover the case of an arbitrary parameter distribution. The obtained equations yield the description of the ensemble dynamics in terms of collective variables and constants of motion. As a particular case of the general setup we consider hierarchically organized ensembles, consisting of a finite number of subpopulations, whereas the number of elements in a subpopulation can be both finite or infinite. Next, we link the Watanabe-Strogatz and Ott-Antonsen theories and demonstrate that the latter one corresponds to a particular choice of constants of motion. The approach is applied to the standard Kuramoto-Sakaguchi model, to its extension for the case of nonlinear coupling, and to the description of two interacting subpopulations, exhibiting a chimera state. With these examples we illustrate that, although the asymptotic dynamics can be found within the framework of the Ott-Antonsen theory, the transients depend on the constants of motion. The most dramatic effect is the dependence of the basins of attraction of different synchronous regimes on the initial configuration of phases.}, language = {en} } @article{PikovskijRosenblum2015, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Dynamics of globally coupled oscillators: Progress and perspectives}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {25}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {9}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4922971}, pages = {11}, year = {2015}, abstract = {In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches. (c) 2015 AIP Publishing LLC.}, language = {en} } @article{RosenblumFruehwirthMoseretal.2019, author = {Rosenblum, Michael and Fr{\"u}hwirth, Martha and Moser, Maximilian and Pikovskij, Arkadij}, title = {Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia}, series = {Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, volume = {377}, journal = {Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, number = {2160}, publisher = {Royal Society}, address = {London}, issn = {1364-503X}, doi = {10.1098/rsta.2019.0045}, pages = {14}, year = {2019}, abstract = {We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.}, language = {en} } @misc{TopcuFruehwirthMoseretal.2018, author = {Top{\c{c}}u, {\c{C}}ağda{\c{s}} and Fr{\"u}hwirth, Matthias and Moser, Maximilian and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Disentangling respiratory sinus arrhythmia in heart rate variability records}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {913}, issn = {1866-8372}, doi = {10.25932/publishup-43631}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436315}, pages = {15}, year = {2018}, abstract = {Objective: Several different measures of heart rate variability, and particularly of respiratory sinus arrhythmia, are widely used in research and clinical applications. For many purposes it is important to know which features of heart rate variability are directly related to respiration and which are caused by other aspects of cardiac dynamics. Approach: Inspired by ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear disentanglement of the heart rate variability into the respiratory-related component and the rest. Main results: The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects. In all cases we show how the disentanglement is manifested in the different measures of heart rate variability. Significance: The suggested technique can be exploited as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate and in cases when effects of other factors on the heart rate variability are in focus.}, language = {en} } @article{TopcuFruehwirthMoseretal.2018, author = {Top{\c{c}}u, {\c{C}}ağda{\c{s}} and Fr{\"u}hwirth, Matthias and Moser, Maximilian and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Disentangling respiratory sinus arrhythmia in heart rate variability records}, series = {Physiological Measurement}, volume = {39}, journal = {Physiological Measurement}, number = {5}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0967-3334}, doi = {10.1088/1361-6579/aabea4}, pages = {12}, year = {2018}, abstract = {Objective: Several different measures of heart rate variability, and particularly of respiratory sinus arrhythmia, are widely used in research and clinical applications. For many purposes it is important to know which features of heart rate variability are directly related to respiration and which are caused by other aspects of cardiac dynamics. Approach: Inspired by ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear disentanglement of the heart rate variability into the respiratory-related component and the rest. Main results: The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects. In all cases we show how the disentanglement is manifested in the different measures of heart rate variability. Significance: The suggested technique can be exploited as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate and in cases when effects of other factors on the heart rate variability are in focus.}, language = {en} } @article{TassRosenblumWeuleetal.1998, author = {Tass, Peter and Rosenblum, Michael and Weule, J. and Kurths, J{\"u}rgen and Pikovskij, Arkadij and Volkmann, J. and Schnitzler, A. and Freund, H.-J.}, title = {Detection of n:m phase locking from noisy data : application to magnetoencephalography}, year = {1998}, abstract = {We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that}, language = {en} } @article{KralemannPikovskijRosenblum2013, author = {Kralemann, Bj{\"o}rn and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Detecting triplet locking by triplet synchronization indices}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {87}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {5}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.052904}, pages = {6}, year = {2013}, abstract = {We discuss the effect of triplet synchrony in oscillatory networks. In this state the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. We suggest an easy to compute measure, a triplet synchronization index, which can be used to detect such states from experimental data.}, language = {en} } @article{PikovskijRosenblum2001, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Detecting direction of coupling in interacting oscillators}, year = {2001}, abstract = {We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.}, language = {en} } @article{RosenblumPikovskij2004, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Delayed feedback control of collective synchrony : an approach to suppression of pathological brain rhythms}, issn = {1063-651X}, year = {2004}, abstract = {We suggest a method for suppression of synchrony in a globally coupled oscillator network, based on the time- delayed feedback via the mean field. Having in mind possible applications for suppression of pathological rhythms in neural ensembles, we present numerical results for different models of coupled bursting neurons. A theory is developed based on the consideration of the synchronization transition as a Hopf bifurcation}, language = {en} } @article{RosenblumPikovskij2004, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Controlling synchronization in an ensemble of globally coupled oscillators}, issn = {0031-9007}, year = {2004}, abstract = {We propose a technique to control coherent collective oscillations in ensembles of globally coupled units (self- sustained oscillators or maps). We demonstrate numerically and theoretically that a time delayed feedback in the mean field can, depending on the parameters, enhance or suppress the self-synchronization in the population. We discuss possible applications of the technique}, language = {en} } @article{Rosenblum2020, author = {Rosenblum, Michael}, title = {Controlling collective synchrony in oscillatory ensembles by precisely timed pulses}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {30}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {9}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/5.0019823}, pages = {9}, year = {2020}, abstract = {We present an efficient technique for control of synchrony in a globally coupled ensemble by pulsatile action. We assume that we can observe the collective oscillation and can stimulate all elements of the ensemble simultaneously. We pay special attention to the minimization of intervention into the system. The key idea is to stimulate only at the most sensitive phase. To find this phase, we implement an adaptive feedback control. Estimating the instantaneous phase of the collective mode on the fly, we achieve efficient suppression using a few pulses per oscillatory cycle. We discuss the possible relevance of the results for neuroscience, namely, for the development of advanced algorithms for deep brain stimulation, a medical technique used to treat Parkinson's disease.}, language = {en} } @article{ZaikinRosenblumLandaetal.1997, author = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen}, title = {Control of noise-induced oscillations of a pendulum with a rondomly vibrating suspension axis}, year = {1997}, language = {en} } @article{BaibolatovRosenblumZhanabaevetal.2010, author = {Baibolatov, Yernur and Rosenblum, Michael and Zhanabaev, Zeinulla Zh. and Pikovskij, Arkadij}, title = {Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling}, issn = {1539-3755}, doi = {10.1103/Physreve.82.016212}, year = {2010}, abstract = {We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically (i) states of complete synchrony, (ii) regimes with coexistence of a synchronous cluster and a drifting subpopulation, and (iii) self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.}, language = {en} } @article{GoldobinPimenovaRosenblumetal.2017, author = {Goldobin, Denis S. and Pimenova, Anastasiya V. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Competing influence of common noise and desynchronizing coupling on synchronization in the Kuramoto-Sakaguchi ensemble}, series = {European physical journal special topics}, volume = {226}, journal = {European physical journal special topics}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2017-70039-y}, pages = {1921 -- 1937}, year = {2017}, abstract = {We describe analytically synchronization and desynchronization effects in an ensemble of phase oscillators driven by common noise and by global coupling. Adopting the Ott-Antonsen ansatz, we reduce the dynamics to closed stochastic equations for the order parameters, and study these equations for the cases of populations of identical and nonidentical oscillators. For nonidentical oscillators we demonstrate a counterintuitive effect of divergence of individual frequencies for moderate repulsive coupling, while the order parameter remains large.}, language = {en} } @article{RosenblumKurthsPikovskij2001, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij}, title = {Comment on "Phase synchronization in discrete chaotic systems"}, year = {2001}, abstract = {Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.}, language = {en} } @article{PikovskijRosenblum2001, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Comment on "Intermittency in chaotic rotations"}, year = {2001}, abstract = {Lai et al. [Phys. Rev. E 62, R29 (2000)] claim that the angular velocity of the phase point moving along the chaotic trajectory in a properly chosen projection (the instantaneous frequency) is intermittent. Using the same examples, namely the R{\"o}ssler and the Lorenz systems, we show the absence of intermittency in the dynamics of the instantaneous frequency.This is confirmed by demonstrating that the phase dynamics exhibits normal diffusion. We argue that the nonintermittent behavior is generic.}, language = {en} } @article{Rosenblum2001, author = {Rosenblum, Michael}, title = {Comment on "Intermittency in chaotic rotations"}, year = {2001}, language = {en} } @article{YeldesbayPikovskijRosenblum2014, author = {Yeldesbay, Azamat and Pikovskij, Arkadij and Rosenblum, Michael}, title = {Chimeralike states in an ensemble of globally coupled oscillators}, series = {Physical review letters}, volume = {112}, journal = {Physical review letters}, number = {14}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.112.144103}, pages = {5}, year = {2014}, abstract = {We demonstrate the emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in nonlocally coupled oscillator lattices. In this regime some part of the ensemble forms a regularly evolving cluster, while all other units irregularly oscillate and remain asynchronous. We argue that the chimera emerges because of effective bistability, which dynamically appears in the originally monostable system due to internal delayed feedback in individual units. Additionally, we present two examples of chimeras in bistable systems with frequency-dependent phase shift in the global coupling.}, language = {en} } @article{TemirbayevNalibayevZhanabaevetal.2013, author = {Temirbayev, Amirkhan A. and Nalibayev, Yerkebulan D. and Zhanabaev, Zeinulla Zh. and Ponomarenko, Vladimir I. and Rosenblum, Michael}, title = {Autonomous and forced dynamics of oscillator ensembles with global nonlinear coupling an experimental study}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {87}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {6}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.062917}, pages = {11}, year = {2013}, abstract = {We perform experiments with 72 electronic limit-cycle oscillators, globally coupled via a linear or nonlinear feedback loop. While in the linear case we observe a standard Kuramoto-like synchronization transition, in the nonlinear case, with increase of the coupling strength, we first observe a transition to full synchrony and then a desynchronization transition to a quasiperiodic state. However, in this state the ensemble remains coherent so that the amplitude of the mean field is nonzero, but the frequency of the mean field is larger than frequencies of all oscillators. Next, we analyze effects of common periodic forcing of the linearly or nonlinearly coupled ensemble and demonstrate regimes when the mean field is entrained by the force whereas the oscillators are not.}, language = {en} } @article{OsipovRosenblumPikovskijetal.1997, author = {Osipov, Grigory V. and Rosenblum, Michael and Pikovskij, Arkadij and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization}, year = {1997}, abstract = {The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.}, language = {en} } @article{ParkRosenblumKurthsetal.1999, author = {Park, Eun Hyoung and Rosenblum, Michael and Kurths, J{\"u}rgen and Zaks, Michael A.}, title = {Alternating locking ratios in imperfect phase synchronization}, year = {1999}, language = {en} } @book{RosenblumKurths1995, author = {Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {A model of neural control of heart rate}, series = {Preprint NLD}, volume = {12}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {22 S.}, year = {1995}, language = {en} } @misc{ClusellaPolitiRosenblum2017, author = {Clusella, Pau and Politi, Antonio and Rosenblum, Michael}, title = {A minimal model of self-consistent partial synchrony (vol 18, 093037, 2016)}, series = {New journal of physics : the open-access journal for physics}, volume = {19}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/aa722b}, pages = {1}, year = {2017}, language = {en} } @misc{ClusellaPolitiRosenblum2016, author = {Clusella, Pau and Politi, Antonio and Rosenblum, Michael}, title = {A minimal model of self-consistent partial synchrony}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe}, number = {890}, issn = {1866-8372}, doi = {10.25932/publishup-43626}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436266}, pages = {19}, year = {2016}, abstract = {We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field.}, language = {en} } @article{ClusellaPolitiRosenblum2016, author = {Clusella, Pau and Politi, Antonio and Rosenblum, Michael}, title = {A minimal model of self-consistent partial synchrony}, series = {NEW JOURNAL OF PHYSICS}, volume = {18}, journal = {NEW JOURNAL OF PHYSICS}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/18/9/093037}, pages = {15}, year = {2016}, abstract = {We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field.}, language = {en} }