Two-attractor chimera and solitary states in a network of nonlocally coupled birhythmic van der Pol oscillators

Abstract

In this paper, a network of van der Pol oscillators with extended nonlinearity is considered in the context of studies on symmetry-breaking phenomena. The van der Pol oscillator with extended nonlinearity has been widely considered as a model for coherent oscillations in enzyme–substrate systems. The particularity of this model is its multistability known as birhythmicity. Due to this feature of the local dynamics, the coupled dynamics shows a rich variety of symmetry-breaking phenomena, among which peculiar chimera and solitary states involving two types of attractors, namely a large limit cycle and a smaller attractor with quasiperiodic-like oscillations. The units of the main incoherent regions of a pattern of this two-attractor chimera evolve only on the large limit cycle whereas those of the main coherent regions evolve only on the smaller attractor. Also, as a consequence of birhythmicity, the mean phase velocity profile of this chimera pattern shows two levels of frequency, each level corresponding to each attractor. On the other hand, the frequencies of oscillations of the solitary units of the solitary states found there are different from the common frequency of oscillations in the coherent cluster, contrary to the classical solitary states for which all the network units are frequency locked. Interestingly, a phenomenon of coupling-induced birhythmicity is found here: two-attractor patterns emerge in the considered network with monorhythmic local dynamics. This study deepens our understanding of patterns formation in coupled multistable systems.