Related papers: Phase Synchronization and invariant measures in si…
Concepts from the Ergodic Theory are used to describe the existence of non-transitive maps in attractors of phase synchronous chaotic systems. It is shown that for a class of phase-coherent systems, e.g. the sinusoidally forced Chua's…
Numerical and experimental evidence is presented to show that many phase synchronized systems of non-identical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the…
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article…
Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting…
We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…
We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
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…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
We investigate the temporal dynamics of the PT-Symmetric nonlinear oscillators in the presence of Duffing nonlinearity for two forms of oscillator configuration. In the former, we consider two oscillator coupled to each other. One…
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…
Phase synchronization is shown to occur between opposite cells of a ring consisting of chaotic Lorenz oscillators coupled unidirectionally through driving. As the coupling strength is diminished, full phase synchronization cannot be…
We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic…
We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an…
We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition…
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…
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses…