Related papers: Collective oscillations in a three-dimensional spi…
We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step…
We study stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we…
We develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations. Collective phase equations describing macroscopic rhythms of the system are derived from Langevin-type…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase…
The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase…
We theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent…
We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical…
Ensembles of alkali or noble-gas atoms at room temperature and above are widely applied in quantum optics and metrology owing to their long-lived spins. Their collective spin states maintain nonclassical nonlocal correlations, despite the…
A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase transition at a critical value of the coupling parameter, leading to stable global…
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. Coupled…
We propose a mean-field theory for nonequilibrium phase transitions to a periodically oscillating state in spin models. A nonequilibrium generalization of the Landau free energy is obtained from the join distribution of the magnetization…
We consider the macroscopic regimes and the scenarios for the onset and the suppression of collective oscillations in a heterogeneous population of active rotators, comprised of excitable or oscillatory elements. We analyze the system in…
We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motivation of this work concerns the case where the individual…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation…
We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with…