Synchronization of Chaos

TL;DR

This paper surveys the theory of synchronization phenomena in chaotic dynamical networks, highlighting their coexistence with chaos and applications in secure communications and parameter estimation.

Contribution

It provides a comprehensive overview of synchronization types in complex networks and discusses their practical applications in various fields.

Findings

Synchronization can coexist with chaos in dynamical networks.

Different types of synchronization are characterized and analyzed.

Applications include secure communications and chaos prediction.

Abstract

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronization, a classical paradigm of order. We survey the main theory behind complete, generalized and phase synchronization phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.