Synchronization transition in space-time chaos in the presence of quenched disorder

TL;DR

This paper investigates how quenched disorder affects the synchronization transition in coupled map lattices, revealing a new universality class with distinct critical exponents across different dimensions.

Contribution

It demonstrates that quenched disorder in coupling is a relevant perturbation, leading to a new universality class with unique critical exponents for synchronization transitions.

Findings

Second-order transition observed with new exponents

Order parameter decays as t^{-} with  depending on the map

Critical exponents are dimension-independent for continuous transitions

Abstract

Synchronization of two replicas of coupled map lattices for continuous maps is known to be in the multiplicative noise universality class. We study this transition in the presence of quenched disorder in coupling. The disorder is identical in both replicas. We study one-dimensional, two-dimensional, and globally coupled logistic and tent maps. We observe a clear second-order transition with new exponents. The order parameter decays as $t^{-\delta}$ and $\delta$ depends on the map and its parameters. The asymptotic order parameter for $\Delta$ distance from a critical point grows as $\Delta^{\beta}$ with $\beta=\delta$. The quenched disorder in coupling is a relevant perturbation for the replica synchronization of coupled map lattices. The critical exponents are different from those of the multiplicative noise universality class. However, it does not depend on dimensionality if the transition is continuous for the cases studied.