相关论文: Clustering in Globally Coupled Oscillators Near a …
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
We study a model of coupled oscillators with bidirectional first nearest neighbours coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major…
When a driven oscillator loses phase-locking to a master oscillator via a Hopf bifurcation, it enters a bounded-phase regime in which its average frequency is still equal to the master frequency, but its phase displays temporal…
Coupled oscillator models where $N$ oscillators are identical and symmetrically coupled to all others with full permutation symmetry $S_N$ are found in a variety of applications. Much, but not all, work on phase descriptions of such systems…
We study two-cluster solutions of an ensemble of generic limit-cycle oscillators in the vicinity of a Hopf bifurcation, i.e. Stuart-Landau oscillators, with a nonlinear global coupling. This coupling leads to conserved mean-field…
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a…
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to…
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
In this paper, we consider a coupled Brusselator model of chemical reactions, for which no symmetry for the coupling matrices is assumed. We show that the model can undergoes a Hopf bifurcation, and consequently periodic solutions can arise…
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we…
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…
Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
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 the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…