Chimera states for directed networks

TL;DR

This paper explores chimera states in directed networks of phase oscillators, revealing how small networks exhibit isolated chimera regions and larger networks form extensive chimera domains, influenced by coupling range.

Contribution

It demonstrates the emergence and evolution of chimera states in directed oscillator networks, including the formation of chimera islands and continents depending on network size and coupling range.

Findings

Chimera islands appear in small networks with unidirectional coupling.

Larger networks merge islands into a continuous chimera continent.

Chimera phenomena diminish with decreasing coupling range.

Abstract

We demonstrate that chimera behavior can be observed in ensembles of phase oscillators with unidirectional coupling. For a small network consisting of only three identical oscillators (cyclic triple), tiny {\it chimera islands} arise in the parameter space. They are surrounded by developed chaotic switching behavior caused by a collision of rotating waves propagating in opposite directions. For larger networks, as we show for hundred oscillators (cyclic century), the islands merge into a single {\it chimera continent} which incorporates the world of chimeras of different configuration. The phenomenon inherits from networks with intermediate ranges of the unidirectional coupling and it diminishes as it decreases.