Related papers: Chaos synchronization in a hyperbolic dynamical sy…
Synchronization among globally coupled, chaotic map lattices can be related to stable periodic windows in isolated chaotic maps. This relation provides a simple predictive tool for the understanding of complicated behavior in coupled…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…
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…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…
It is shown that the synchronization behavior of a system of chaotic maps subject to either an external forcing or a coupling function of their internal variables can be inferred from the behavior of a single element in the system, which…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a…
In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is…
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our…
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…
This paper deals with the chaotic oscillator synchronization. A new approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by…
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size…
We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to…
We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues…
This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
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…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…