Phase chimera states: frozen patterns of disorder

TL;DR

This paper introduces and analyzes a new type of pattern called phase chimera states in coupled Stuart-Landau oscillators, where amplitude remains constant but phase coherence varies, revealing complex coexistence of synchronized and incoherent groups.

Contribution

The study uncovers and characterizes the stable phase chimera states in Stuart-Landau oscillators, expanding understanding of pattern formation beyond phase-only models.

Findings

Existence of stable phase chimera states with identical amplitudes.

Identification of multitailed phase chimera states with multiple incoherent groups.

Insights into the dynamics of oscillators with variable amplitudes.

Abstract

Coupled oscillators can serve as a testbed for larger questions of pattern formation across many areas of science and engineering. Much effort has been dedicated to the Kuramoto model and phase oscillators, but less has focused on oscillators with variable amplitudes. Here we examine the simplest such oscillators -- Stuart-Landau oscillators -- and attempt to elucidate some puzzling dynamics observed in simulation by us and others. We demonstrate the existence and stability of a previously unreported state which we call a ``phase chimera state.'' Remarkably, in this state, the amplitudes of all oscillators are identical, but one subset of oscillators phase-locks while another subset remains incoherent in phase. We also show that this state can take the form of a ``multitailed phase chimera state'' where a single phase-synchronous cluster of oscillators coexists with multiple groups of phase-incoherent oscillators.