Chaotic Chimera Attractors in a Triangular Network of Identical Oscillators

TL;DR

This paper reveals the existence of macroscopic chaotic chimera attractors in a three-population network of identical oscillators, demonstrating complex aperiodic dynamics and coexistence with other stable chimera states.

Contribution

It extends the understanding of chimera states by showing chaotic attractors in the full phase space of a three-population oscillator network, beyond the reduced manifold.

Findings

Chaotic chimera states exhibit aperiodic antiphase dynamics.

Coexistence of chaotic, periodic, and stationary chimera states.

Chaotic chimeras are observed both in finite systems and the thermodynamic limit.

Abstract

A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains, known as chimera states. Chimera states exhibit various macroscopic dynamics with different motions of the Kuramoto order parameter. Stationary, periodic and quasiperiodic chimeras are known to occur in two-population networks of identical phase oscillators. In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically [Phys. Rev. E 82, 016216 (2010)]. In this paper, we study the full phase space dynamics of such three-population networks. We demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. We observe these chaotic chimera states in both finite-sized systems and the thermodynamic limit outside the Ott-Antonsen manifold. The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tri-stability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold.