Universal Critical Behavior of the Synchronization Transition in Delayed Chaotic Systems

TL;DR

This paper demonstrates that the synchronization transition in coupled delayed chaotic systems exhibits universal critical behavior, aligning with the bounded KPZ universality class, and discusses potential emergence of directed percolation behavior in nonlinear regimes.

Contribution

It reveals the universal critical properties of synchronization transitions in delayed chaotic systems and maps them to known universality classes, extending understanding of complex system synchronization.

Findings

Synchronization transition is absorbing.

Transitions belong to the bounded KPZ universality class.

Directed percolation behavior may occur with strong nonlinearities.

Abstract

We numerically investigate the critical behavior of the synchronization transition of two unidirectionally coupled delayed chaotic systems. We map the problem to a spatially extended system to show that the synchronization transition in delayed systems exhibits universal critical properties. We find that the synchronization transition is absorbing and generically belongs to the universality class of the bounded Kardar-Parisi-Zhang equation, as occurs in the case of extended systems. We also argue that directed percolation critical behavior may emerge for systems with strong nonlinearities