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

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.

Automated summary

The study investigates bump states in an array of active rotators coupled by nonlocal attraction and global repulsion, demonstrating how they can emerge from completely coherent Turing patterns and eventually transform into extensive chaos with many incoherent units. Different types of transitions are presented, explaining the formation of coherence-incoherence patterns based on the classical paradigm of short-range activation and long-range inhibition.