@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{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{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{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{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} }