Hyperbolic chaos at blinking coupling of noisy oscillators

TL;DR

This paper investigates hyperbolic chaos in an ensemble of noisy phase oscillators with blinking mean-field coupling, revealing chaotic dynamics in the order parameters and confirming hyperbolicity through numerical tests.

Contribution

It demonstrates hyperbolic chaos in noisy oscillators with blinking coupling and confirms hyperbolicity via Lyapunov analysis, advancing understanding of chaotic dynamics in such systems.

Findings

Order parameters exhibit hyperbolic chaos.

Chaotic phases follow a Bernoulli map.

Finite-size effects slightly smear chaos.

Abstract

We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations.