Between Synchrony and Turbulence: Intricate Hierarchies of Coexistence Patterns

TL;DR

This paper explores complex coexistence patterns in globally coupled identical oscillators, revealing a hierarchy of states from synchrony to chaos, including chimera states as intermediate phenomena.

Contribution

It introduces a comprehensive hierarchy of coexistence states in coupled oscillators, extending beyond chimera states to include chaotic and fully incoherent regimes.

Findings

Hierarchy of coexistence patterns identified

Chimera states are part of a transition to chaos

States evolve through attractor collisions leading to incoherence

Abstract

Coupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of so-called chimera states, states of coexisting synchronized and unsynchronized oscillators, provided a possible link between the two and definitely showed that different parts of the same ensemble can sustain qualitatively different forms of motion. Here, we demonstrate that globally coupled identical oscillators can express a range of coexistence patterns more comprehensive than chimeras. A hierarchy of such states evolves from the fully synchronized solution in a series of cluster-splittings. At the far end of this hierarchy, the states further collide with their own mirror-images in phase space -- rendering the motion chaotic, destroying some of the clusters and thereby producing even more intricate coexistence patterns. A sequence of such attractor collisions can ultimately lead to full incoherence of only single asynchronous oscillators. Chimera states, with one large synchronized cluster and else only single oscillators, are found to be just one step in this transition from low- to high-dimensional dynamics.