相关论文: Exactly solvable phase oscillator models with sync…

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…

This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled…

We consider a population of globally coupled oscillators in which phase shifts in the coupling are random. We show that in the maximally disordered case, where the pairwise shifts are i.i.d. random variables, the dynamics of a large…

We propose a population model for $\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term.…

We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…

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…

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…

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are…

In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random…

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…

Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the…

We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven…

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 study a chain of $N+1$ phase oscillators with asymmetric but uniform coupling. This type of chain possesses $2^{N}$ ways to synchronize in so-called travelling wave states, i.e. states where the phases of the single oscillators are in…

We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…

An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…

Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…

Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…

We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…