Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata

TL;DR

This paper reviews recent numerical studies on the collective behavior of coupled maps and automata, focusing on second-order dynamics and quasiperiodic order parameters in many-body systems.

Contribution

It introduces a second-order difference equation framework to describe the global temporal properties of synchronized states in coupled dynamical systems.

Findings

Identification of quasiperiodic order parameters with irrational frequencies

Demonstration of thermodynamic noise superimposed on collective states

Use of second-order difference equations to model global dynamics

Abstract

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.