Phase ordering induced by defects in chaotic bistable media

The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin variables that define the phases. It is found that spatial defects can induce the formation of domains in bistable spatiotemporal systems. The minimum distance between defects acts as parameter for a transition from a homogeneous state to a heterogeneous regime where two phases coexist The critical exponent of this transition also exhibits a transition when the coupling is increased, indicating the presence of a new class of domain where both phases coexist forming a chessboard pattern. Coupled map lattices constitute fruitful and computationally efficient models for the study of a variety of dynamical processes in spatially distributed systems [1]. The discrete-space character of coupled map systems makes them specially appropriate for the investigation of spatiotemporal dynamics on nonuniform and on complex networks [2–5]. There has been recent interest in the study of the phase-ordering properties of systems of coupled chaotic maps and their relationship with Ising models in statistical physics [6– 12]. These works have generally assumed the phase competition dynamics taking place on a uniform space; however, in many physical situations the medium that supports the dynamics can be nonuniform due to the intrinsic heterogeneous nature of the substratum such as porous or fractured media, or it may arise from random fluctuations in the medium. This paper investigates the process of phase ordering in coupled chaotic maps on a lattice with defects as a model for studying this phenomenon on nonuniform media. We consider a system of coupled maps defined on a two-dimensional square lattice of size N = L × L with periodic boundary conditions and having randomly distributed defects, as shown in Fig. 1. A defect is a non-active site, i.e., a site that possesses no dynamics. The density of defects in the lattice is characterized in terms of the minimum Euclidean distance d between defects. The dynamics of the diffusively coupled map system is described by xi(t+ 1) = (1 − ǫ)f(xi(t)) + ǫ Ni ∑ j∈νi f(xj(t)) , (0.1) where xi(t) is the state of an active site i (i = 1, . . . , N) at time t, νi is the set of the nearest neighbors of site i and Ni ∈ {1, 2, 3, 4} is the cardinality of this set, ǫ measures the coupling Pr1-2 JOURNAL DE PHYSIQUE IV strength, and f(x(t)) is a chaotic map that expresses the local bistable dynamics [7, 8],