Related papers: Global dynamics of oscillator populations under co…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…
Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…
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 investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…
We study an ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate, that if the oscillators are forced in several harmonics, stationary synchronous regimes can be…
The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that…
In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…
We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble…
Driven by various kinds of noise, ensembles of limit cycle oscillators can synchronize. In this letter, we propose a general formulation of synchronization of the oscillator ensembles driven by common colored noise with an arbitrary power…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
Watanabe-Strogatz theory provides a low-dimensional description of identical Kuramoto oscillators via the framework of the M\"obius transformation. Here, using the Watanabe-Strogatz theory, we provide a unifying description for a broad…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
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…
The universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described. The reasons of the generalized synchronization occurrence may be clarified by…
Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central…
We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the…
We analyze the noise induced synchronization between a collective variable characterizing a complex system with a finite number of interacting bistable units and time periodic driving forces. A random phase process associated to the…