Synchronization of oscillators with hyperbolic chaotic phases

TL;DR

This paper investigates synchronization phenomena in oscillators with hyperbolic chaotic phases using two models, revealing bistability and complex transition behaviors as coupling strength varies.

Contribution

It introduces two models of hyperbolic chaotic oscillators and analyzes their synchronization dynamics, including bistability and complex intermediate states.

Findings

Bistability between synchrony and disorder in one model.

Complete synchrony at high coupling in the second model.

Complex intermediate dynamics of the order parameter.

Abstract

Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses an Ott-Antonsen invariant manifold, allowing for a derivation of a map for the evolution of the complex order parameter. Beyond a critical coupling strength, this model demonstrates bistability synchrony-disorder. Another model is based on the coupled autonomous oscillators with hyperbolic chaotic strange attractors of Smale-Williams type. Here a disordered asynchronous state at small coupling strengths, and a completely synchronous state at large couplings are observed. Intermediate regimes are characterized by different levels of complexity of the global order parameter dynamics.