Related papers: Comment on ``Phase ordering in chaotic map lattice…
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 present some result about phase separation in coupled map lattices with additive noise. We show that additive noise acts as an ordering agent in this class of systems. In particular, in the weak coupling region, a suitable quantity of…
The problem of synchronization of coupled Hamiltonian systems exhibits interesting features due to the non-uniform or mixed nature (regular and chaotic) of the phase space. We study these features by investigating the synchronization of…
We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter…
Coupled map lattices are paradigmatic models of many collective phenomena. However, quite different patterns can emerge depending on the updating scheme. While in early versions, maps were updated synchronously, there has been in recent…
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…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
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…
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 show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
A consistent perturbation theory expansion is presented for phase-ordering kinetics in the case of a nonconserved scalar order parameter. At zeroth order in this expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic…
A consistent perturbation theory expansion is presented for phase ordering kinetics in the case of a nonconserved scalar order parameter. At lowest order in this formal expansion one obtains the theory due to Ohta, Jasnow and Kawasaki…
We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…
The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the…
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…