Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice (original) (raw)
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Synchronization and suppression of chaos in non-locally coupled map lattices
Pramana, 2009
We considered coupled map lattices with long-range interactions to study the spatiotemporal behaviour of spatially extended dynamical systems. Coupled map lattices have been intensively investigated as models to understand many spatiotemporal phenomena observed in extended system, and consequently spatiotemporal chaos. We used the complex order parameter to quantify chaos synchronization for a one-dimensional chain of coupled logistic maps with a coupling strength which varies with the lattice in a powerlaw fashion. Depending on the range of the interactions, complete chaos synchronization and chaos suppression may be attained. Furthermore, we also calculated the Lyapunov dimension and the transversal distance to the synchronization manifold.
Zero delay synchronization of chaos in coupled map lattices
Physical Review E, 2007
We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.
Synchronization Phenomena of Chaotic Map Lattice with Time Varying Coupling
2007
Synchronization phenomena based upon of globally coupled maps are studied in many fields of natural science. In this contribution, we study synchronization phenomena in chaotic map lattices with time varying couplings. By computer simulations, we confirm the presence of the switching synchronization.
Synchronous chaos in coupled map lattices with small-world interactions
Physical Review E, 2000
In certain physical situations, extensive interactions arise naturally in systems. We consider one such situation, namely, small-world couplings. We show that, for a fixed fraction of nonlocal couplings, synchronous chaos is always a stable attractor in the thermodynamic limit. We point out that randomness helps synchronization. We also show that there is a size dependent bifurcation in the collective behavior in such systems.
Spatiotemporal chaos in one- and two-dimensional coupled map lattices
Physica D: Nonlinear Phenomena, 1989
Coupled map lattices are investigated as a model for spatiotemporal chaos. Pattern dynamics in diffusivel~y coupled logistic lattice is briefly reviewed with the use of power spectra, domain distribution, a~d Lyapunov spectra. Mechanism of pattern selection with the suppression of chaos is discussed. Pattern dynamics on a 2-dimensional lattice is shown, in a weak coupling regime, a similarity with the one-dimensional case is found; frozen random pattern, pattern selection, Brownian motion of a chaotic string, and intermittent collapse of the pattern with selective flicker noise. In a strong coupling regime, frozen pattern is found to be unstable by the surface tension, which is in contrast with the one-dimensional case. Convective coupling model is introduced in connection with the fluid turbulence of Navier-Stokes type. Soliton turbulence and vortex turbulence in the model are reported. Physical implications of coupled map lattices are discussed.
Dynamics of chaos-order interface in coupled map lattices
Physica D: Nonlinear Phenomena, 1997
We study a coupled map lattice model with two states: a simple fixed point and spatio-temporal chaos. Preparing properly initial conditions, we investigate the dynamics of the interface between order and chaos. In the one-dimensional lattice regimes of irregular and regular front propagation behavior are observed and analyzed by introducing a local front map and a front Lyapunov exponent. Corresponding to these different regimes of front propagation we can characterize different types of transitions from laminar state to chaos using comoving Lyapunov exponents. In the two-dimensional lattice these types of front motion are related to regimes of roughening and flattening of the interface.
Synchronization and Phase Ordering in Globally Coupled Chaotic Maps
Springer Proceedings in Mathematics & Statistics, 2015
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 parameters of the system. The collective properties of the system are characterized by means of the persistence probability of equivalent spin variables that define two phases, and by a magnetization-like order parameter that measures the phase-ordering behavior. As a consequence of the global interaction, the persistence probability saturates for all values of the coupling parameter, in contrast to the transition observed in the temporal behavior of the persistence in coupled maps on regular lattices. A discontinuous transition from a non-ordered state to a collective phase-ordered state takes place at a critical value of the coupling. On an interval of the coupling parameter, we find three distinct realizations of the phase-ordered state, which can be discerned by the corresponding values of the saturation persistence. Thus, this statistical quantity can provide information about the transient behaviors that lead to the different phase configurations in the system. The appearance of disordered and phase-ordered states in the globally coupled system can be understood by calculating histograms and the time evolution of local map variables associated to the these collective states.
Transversal dynamics of a non-locally-coupled map lattice
Physical Review E, 2007
A lattice of coupled chaotic dynamical systems may exhibit a completely synchronized state, which defines a low-dimensional invariant manifold in phase space. However, the high dimensionality of the latter typically yields a complex dynamics with many features like chaos suppression, quasiperiodicity, multistability, and intermittency. Such phenomena are described by considering the transversal dynamics to the synchronization manifold for a coupled logistic map lattice with a long-range coupling prescription.
Physica A: Statistical Mechanics and its Applications, 2006
Spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales, characterized by repeated conversions from spatially localized transient chaos into global laminar patterns. A simple model, yet retaining some features of more complex systems, consists of a lattice of a class of tent maps with an escaping region. The coupling prescription we adopt in this work considers the interaction of a site with all its neighbors, the corresponding strength decaying with the lattice distance as a power-law. This makes possible to pass continuously from a local (nearest-neighbor) to a global kind of coupling. We investigate statistical properties of both the chaotic transient bursts and the periodic laminar states, with respect to the coupling parameters.