Related papers: Synchronization of Coupled Boolean Phase Oscillato…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
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…
We considered the phase coherence dynamics in a Two-Frequency and Two-Coupling (TFTC) model of coupled oscillators, where coupling strength and natural oscillator frequencies for individual oscillators may assume one of two values…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or…
We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply-peaked quasi-extended modes.…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We examine the dynamics of an ensemble of phase oscillators that are divided in $k$ sets, with time-delayed coupling interactions {\em only} between oscillators in different sets or partitions. The network of interactions thus form a…
We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…
We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
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…
In principle, while coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators.…