Extreme value theory for synchronization of coupled map lattices,

TL;DR

This paper links the probability of synchronization in chaotic coupled map lattices to extreme value laws, providing a detailed probabilistic description supported by numerical computations applicable to real systems.

Contribution

It establishes a connection between synchronization probability and extreme value theory, introducing the extremal index as a key parameter for analysis.

Findings

Synchronization probability relates to the distribution of maximum observables.

Extreme value laws describe the distribution of maxima in the system.

Numerical results support theoretical predictions and extend applicability.

Abstract

We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to the family of extreme value laws, whose parameters, namely the extremal index, allow us to get a detailed description of the probability of synchronisation. Theoretical results are supported by robust numerical computations that allow to go beyond the theoretical framework provided and are potentially applicable to physically relevant systems.