Chimeralike states in a network of oscillators under attractive and repulsive global coupling

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.