Condensation versus independence in weakly interacting CMLs

TL;DR

This paper introduces a unified model for large multicomponent systems that can exhibit both synchronization and independent behaviors depending on interaction properties, offering new insights into weakly interacting coupled map lattices.

Contribution

It unifies IPS and CML approaches and reveals conditions under which weak interactions lead to condensation or independence, challenging the assumption of generic independence.

Findings

Model demonstrates both synchronization and independence behaviors.

Interaction potential properties determine system dynamics.

Provides new perspective on synchronization in dynamical networks.

Abstract

We propose a simple model unifying two major approaches to the analysis of large multicomponent systems: interacting particle systems (IPS) and couple map lattices (CML) and show that in the weak interaction limit depending on fine properties of the interaction potential this model may demonstrate both condensation/synchronization and independent motions. Note that one of the main paradigms of the CML theory is that the latter behavior is supposed to be generic. The model under consideration is related to dynamical networks and sheds a new light to the problem of synchronization under weak interactions.