Related papers: Phase Synchronization and Polarization Ordering of…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
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…
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…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
Over the last half century the liquid-gas phase transition and the magnetization phase transition have come to be well understood. After an order parameter, $r$, is defined, it can be derived how $r=0$ for $T>T_c$ and how $r \propto (T_c -…
We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the…
We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined…
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…
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,…
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…
We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is…
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…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…
We investigate a system of four nearest neighbour bidirectional coupled phase oscillators of dissimilar initial frequencies in a ring at the changeover into a synchronizing state. There are twenty four permutations upon assigning 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 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…