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

Franović, Igor; Omel'chenko, Oleh E.; Wolfrum, Matthias

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

Files

Franovic2021_PhysRevE104.pdf(1.1 MB)

Date

2021-11-04

Authors

Franović, Igor

Omel'chenko, Oleh E.

Wolfrum, Matthias

Journal Title

Physical Review E

Volume Title

104

Article Title

L052201

Publisher

American Physical Society (APS)

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 nonlocal attraction and global repulsion. We demonstrate how they can emerge in a supercritical scenario from completely coherent Turing patterns: a single incoherent unit appears in a homoclinic bifurcation, undergoing subsequent transitions to quasiperiodic and chaotic behavior, which eventually transforms 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.