@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{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{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{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} }