@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} } @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} } @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} } @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} }