Amplitude and phase chimera states and cross-correlations in a ring of nonlocally coupled chaotic systems

Abstract:

In the present talk we introduce the basic models for individual elements of ensembles of nonlocally coupled chaotic maps, namely, the two-dimensional Henon map and two-dimensional Lozi map. The first map describes the typical properties of oscillators with non-hyperbolic chaotic attractors, while the second one -- with hyperbolic attractors. We substantiate the hypothesis about the role of hyperbolicity in the appearance of chimera states. Particularly, the “coherence-incoherence” transition is explored in a ring of nonlocally coupled Lorenz oscillators. It is shown that in an ensemble of Lorenz oscillators in the regime of hyperbolic chaos, the transition from coherence to incoherence is observed through solitary states (there are no chimera states), while in the regime of non-hyperbolic attractor, chimera states can be observed.

We also explore the bifurcation transition from coherence to incoherence in an ensemble of nonlocally coupled logistic maps. It is shown that two types of chimera states, namely, amplitude and phase, can be found in this network. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the conditions for realizing the chimera states in the ensemble. The regularities are established for the evolution of cross-correlations of oscillations in the network elements at the bifurcations related to the coupling strength variation. We reveal the features of cross-correlations for phase and amplitude chimera states. It is also shown that the effect of time intermittency between the amplitude and phase chimeras can be realized in the considered ensemble.