Related papers: Pattern Formation in a Two-Dimensional Array of Os…

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…

Coupled arrays of Andronov-Hopf oscillators are investigated. These arrays can be diffusively or repulsively coupled, and can serve as central pattern generator models in animal locomotion and robotics. It is shown that repulsive coupling…

We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between…

We study a network of 500 coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all…

We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures…

A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise.…

We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.

We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns…

We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…

A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…

Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…

We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected…

We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence…

We report the appearance and the metamorphoses of spiral wave chimera states in coupled phase oscillators with inertia. First, when the coupling strength is small enough, the system behavior resembles classical two-dimensional (2D)…

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…

By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…

Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…

Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the…

We study the dynamical behavior of an ensemble of oscillators interacting through short range bidirectional pulses. The geometry is 1D with periodic boundary conditions. Our interest is twofold. To explore the conditions required to reach…