Bumps, chimera states, and Turing patterns in systems of coupled active rotators

TL;DR

This paper investigates the emergence of bump, chimera, and Turing patterns in coupled active rotators, revealing how complex coherence-incoherence patterns arise through bifurcations and chaos in non-locally coupled systems.

Contribution

It introduces a novel analysis of bump states in active rotators with non-local attraction and global repulsion, linking pattern formation to classical activation-inhibition mechanisms.

Findings

Bumps emerge from supercritical Turing patterns via bifurcations.

Incoherent units appear through homoclinic bifurcations and chaos.

Various transition pathways to coherence-incoherence patterns are identified.

Abstract

Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units similar patterns, where coherent units are at rest, are called bump states. Here, we study bumps in an array of active rotators coupled by non-local attraction and global repulsion. We demonstrate how they can emerge in a supercritical scenario from completely coherent Turing patterns: single incoherent units appear in a homoclinic bifurcation with a subsequent transition via quasiperiodic and chaotic behavior, eventually transforming into extensive chaos with many incoherent units. We present different types of transitions and explain the formation of coherence-incoherence patterns according to the classical paradigm of short-range activation and long-range inhibition.