TY - JOUR A1 - Temirbayev, Amirkhan A. A1 - Nalibayev, Yerkebulan D. A1 - Zhanabaev, Zeinulla Zh. A1 - Ponomarenko, Vladimir I. A1 - Rosenblum, Michael T1 - Autonomous and forced dynamics of oscillator ensembles with global nonlinear coupling an experimental study JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevE.87.062917 SN - 1539-3755 SN - 1550-2376 VL - 87 IS - 6 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Montaseri, Ghazal A1 - Yazdanpanah, Mohammad Javad A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - Synchrony suppression in ensembles of coupled oscillators via adaptive vanishing feedback JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1063/1.4817393 SN - 1054-1500 VL - 23 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Kralemann, Björn A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - Detecting triplet locking by triplet synchronization indices JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevE.87.052904 SN - 1539-3755 VL - 87 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Kralemann, Bjoern A1 - Fruehwirth, Matthias A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael A1 - Kenner, Thomas A1 - Schaefer, Jochen A1 - Moser, Maximilian T1 - In vivo cardiac phase response curve elucidates human respiratory heart rate variability JF - Nature Communications N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1038/ncomms3418 SN - 2041-1723 VL - 4 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Ehrich, Sebastian A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - From complete to modulated synchrony in networks of identical Hindmarsh-Rose neurons JF - European physical journal special topics N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1140/epjst/e2013-02025-8 SN - 1951-6355 SN - 1951-6401 VL - 222 IS - 10 SP - 2407 EP - 2416 PB - Springer CY - Heidelberg ER -