Mean field theory of critical coupled map lattices

TL;DR

This paper develops a mean-field theoretical framework for coupled map lattices undergoing phase transitions, showing critical exponents match equilibrium statistical mechanics and closely aligning with numerical simulations.

Contribution

It introduces a single-site approximation for the Perron-Frobenius equation in coupled map lattices and demonstrates its effectiveness in predicting critical behavior.

Findings

Critical exponents match those of equilibrium mean-field theory.

Critical coupling g_c closely agrees with numerical simulations.

The approach provides a theoretical basis for phase transition analysis in coupled map lattices.

Abstract

We study the single-site approximation of the Perron-Frobenius equation for a coupled map lattice exhibiting a phase transition at a critical value g_c of the coupling constant. We found that the critical exponents are the same as in the usual mean-field theory of equilibrium statistical mechanics. Remarkably, the value of g_c is within six percent of the one previously obtained by numerical simulations with asynchronous updating.