Phase Ordering and Onset of Collective Behavior in Chaotic Coupled Map Lattices

TL;DR

This paper investigates how phase ordering and collective behavior emerge in chaotic coupled map lattices as the coupling strength varies, revealing algebraic scaling and continuous exponents related to known theoretical models.

Contribution

It identifies the critical coupling value for collective behavior onset and characterizes the scaling properties and exponents during phase ordering in chaotic lattices.

Findings

Multistability disappears beyond a critical coupling strength g_e.

Pattern length and spin variables scale algebraically with time.

Exponents vary continuously with g and relate to Ginzburg-Landau theory.

Abstract

The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective behavior is observed. The persistence of equivalent discrete spin variables and the characteristic length of the patterns observed scale algebraically with time during phase ordering. The associated exponents vary continuously with $g$ but remain proportional to each other, with a ratio close to that of the time-dependent Ginzburg-Landau equation. The corresponding individual values seem to be recovered in the space-continuous limit.