Chimera states formed via a two-level synchronization mechanism

Abstract

We introduce an oscillatory toy-model with variable frequency governed by a 3rd order equation to shed light on the formation of chimera states in systems of coupled oscillators. The toy-oscillators are constructed as bistable units and depending on the initial conditions their frequency may result in one of the two attracting fixed points, and (two-level synchronization). Numerical simulations demonstrate that when these oscillators are nonlocally coupled in networks, they organize in domains with alternating frequencies. In each domain the oscillators synchronize, while sequential domains follow different modes of synchronization. The border elements between two consecutive domains form the asynchronous domains as they are influenced by both frequencies. This way chimera states are formed via a two-level synchronization scenario. We investigate the influence of the frequency coupling constant and of the coupling range on the chimera morphology and we show that the chimera multiplicity decreases as the coupling range increases.The frequency spectrum is calculated in the coherent and incoherent domains of this model. In the coherent domains single frequencies ( or ) are observed, while in the incoherent domains both and as well as their superpositions appear. This mechanism of creating domains of alternating frequencies offers a reasonable generic scenario for chimera state formation.