Chimera structures in ensembles of nonlocally coupled Sprott maps

Background and Objectives: Recently, special attention in nonlinear dynamics and related research fields was targeted to the study of chimera states in networks of coupled oscillators. Chimeras were revealed in ensembles of nonlocally coupled identical systems which are described by both discrete- and continuous-time chaotic systems. In the paper we study numerically the dynamics of ring networks of nonlocally coupled chaotic discrete maps in order to find chimera states of different types, namely, phase and amplitude chimeras. The local dynamics of the individual elements is described by 2D and 3D Sprott maps which exhibit a quasi-periodic route to chaos and the regime of hyperchaos. Materials and Methods: The analysis is carried out using a software package which was elaborated for modeling the dynamics of complex networks. This program entitled “Computer program for modeling networks of dynamical elements, which are described by one-dimensional or two-dimensional coupling matrices” got the Certificate on state registration of a computer program. This software enables one to perform a detailed study of the spatio-temporal dynamics of the considered networks as the parameters of the individual elements and of the nonlocal coupling are varied, as well as to construct instantaneous profiles (snapshots) and space-time plots for the ensemble dynamics. Results: The numerical analysis of the dynamics of the ensembles of nonlocally coupled 2D and 3D Sprott maps has shown that the transition from complete chaotic synchronization to the regime of spatio-temporal chaos occurs through the appearance of chimera structures. For certain values of the coupling range and when decreasing coupling strength, the ring of 2D Sprott maps demonstrates amplitude chimera structures, whose elements are characterized by strongly developed chaotic behavior. The regime of coexistence of phase and amplitude chimeras is observed in the network of 3D Sprott maps with nonlocal coupling. Conclusion: The numerical results obtained and described in this paper indicate that the regimes of phase and amplitude chimeras in ensembles of nonlocally coupled chaotic oscillators are typical not only for the case when individual oscillators are characterized by perioddoubling bifurcations, but also for the oscillators which demonstrate the quasi-periodic route to chaos.