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We present numerical results for a set of bifurcations occurring at the transition from complete chaotic synchronization to spatio-temporal chaos in a ring of nonlocally coupled chaotic logistic maps. 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 distinctive 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.

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We study numerically the dynamics of a network made of two coupled one-dimensional ensembles of discrete-time systems. The first ensemble is represented by a ring of nonlocally coupled Henon maps, and the second one -by a ring of nonlocally coupled Lozi maps. We find that the network of coupled ensembles can realize all the spatio-temporal structures which are observed both in the Henon map ensemble and in the Lozi map ensemble when uncoupled. Moreover, we reveal a new type of spatiotemporal structure, a solitary state chimera, in the considered network. We also establish and describe the effect of mutual synchronization of various complex spatiotemporal patterns in the system of two coupled ensembles of Henon and Lozi maps.PACS numbers: 05.45.-a, 02.60.-x Keywords: ensemble of nonlocally coupled oscillators, multilayer systems, chimera states, synchronization of spatiotemporal structures, synchronization region, inertial and dissipative couplingRecently studying the formation and evolution of various spatiotemporal patterns in ensembles or networks of coupled oscillators has become one of the most rapidly developing and highly attractive research topics in the nonlinear science and its applications. This exclusive interest is especially related to the discovery of a novel type of spatiotemporal structure -a chimera state. A lot of attention is paid to the dynamics of coupled ensembles of identical elements with various coupling topologies, but of particular interest are coupled ensembles with different types of network elements. In the latter case, the enrichment of regimes as well as the synchronization of spatiotemporal patterns is expected to be observed.In the present paper we analyze the spatiotemporal dynamics of a network made of two coupled rings of Henon and Lozi maps with nonlocal coupling. Our numerical studies have shown that this network can demonstrate both the spatiotemporal regimes, which are observed in separate rings, and a new type of chimera structure, called a solitary state chimera. We have also established the possibility of realizing the mutual synchronization of various complex spatiotemporal structures in the network of two coupled rings. The identity of synchronous patterns is confirmed by calculating the cross-correlation coefficient. The existence of a finite region of synchronization in the coupling parameters plane of the considered system is shown for an exemplary synchronous structure.

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We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.

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