Chimera and Phase Cluster States in Populations of Coupled Chemical Oscillators

Populations of coupled oscillators may exhibit two coexisting subpopulations, one with synchronized oscillations and the other with unsynchronized oscillations, even though all of the oscillators are coupled to each other in an equivalent manner. This phenomenon, discovered about ten years ago in theoretical studies by Kuramoto and Battogtokh [1], was further characterized by Abrams and Strogatz [2] and named the chimera state after the Greek mythological creature made up of different animals. The highly counterintuitive coexistence of coherent and incoherent oscillations in populations of identical oscillators, each with an equivalent coupling structure, inspired great interest and a flurry of theoretical activity [3–19]. Here we report on experimental studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators. Our experiments with coupled Belousov-Zhabotinsky (BZ) oscillators [20, 21] and corresponding simulations reveal chimera behavior that differs significantly from behavior found in theoretical studies of phase oscillator models. Following Abrams et al. [5], we study a system with two subpopulations of oscillators that are globally coupled, both within and between the subpopulations. Like the original model of Kuramoto and Battogtokh [1], in which each oscillator has an equivalent coupling structure, with coupling strength decreasing exponentially with distance, each oscillator in the model by Abrams et al. [5] has an equivalent coupling structure, with stronger global coupling to its fellow subpopulation members and weaker global coupling to the oscillators in the other subpopulation. Both models systems are multistable, with the fully synchronized state exhibited for homogeneous initial conditions and the chimera state exhibited for particular heterogeneous initial conditions [4, 5].