@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{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{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{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} } @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} } @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{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} } @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{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} }