Related papers: Global Analysis of Synchronization in Coupled Maps
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
We study self-organized (s-) and driven (d-) synchronization in coupled map networks for some simple networks, namely two and three node networks and their natural generalization to globally coupled and complete bipartite networks. We use…
An approach based on the kernel methods for capturing the nonlinear interdependence between two signals is introduced. It is demonstrated that the proposed approach is useful for characterizing generalized synchronization with a successful…
An asynchronous parallel version of the non-intrusive global-local coupling is implemented. The case of many patches, including those covering the entire structure, is studied. The asynchronism limits the dependency on communications,…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Generalized synchronization is plausibly the most complex form of synchronization. Previous studies have revealed the existence of weak or strong forms of generalized synchronization depending on the multi- or mono-valued nature of the…
It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…
A novel approach is being developed to introduce a parallel asynchronous implementation of non-intrusive global-local coupling. This study examines scenarios involving numerous patches, including those covering the entire structure. By…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
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…
We study a network of finitely many interacting clusters where each cluster is a collection of globally coupled circle maps in the thermodynamic (or mean field) limit. The state of each cluster is described by a probability measure, and its…
We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in…
A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several…
We study the synchronization of a coupled map lattice consisting of a one-dimensional chain of logistic maps. We consider global coupling with a time-delay that takes into account the finite velocity of propagation of interactions. We…
We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete…
A system of four globally coupled doubling maps is studied in this paper. It is known that such systems have a unique absolutely continuous invariant measure (acim) for weak interaction, but the case of stronger coupling is still…
We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite…
We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability…