Spiral wave patterns in two-layer 2D lattices of nonlocally coupled discrete oscillators. Synchronization of spiral wave chimeras

The paper describes the spatio-temporal dynamics of a lattice that is given by a 2D $N \times N$ network of nonlocally coupled Nekorkin maps which model neuronal activity. The network behavior is studied for periodic and no-flux boundary conditions. It is shown that for certain values of the coupling parameters, rotating spiral waves and spiral wave chimeras can be observed in the considered lattice. We analyze and compare statistical and dynamical characteristics of the local oscillators from coherence and incoherence clusters of a spiral wave chimera. Furthermore, effects of mutual and external synchronization of spiral wave structures in two coupled such lattices are studied. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of their synchronization. Our numerical studies indicate that when the coupling strength between the lattices is sufficiently weak, only a certain part of oscillators of the interacting networks is imperfectly synchronized, while the other part demonstrates a partially synchronous behavior. If the spatiotemporal patterns in the lattices do not include incoherent cores, imperfect synchronization is realized for most oscillators above a certain value of the coupling strength. In the regime of spiral wave chimeras, the imperfect synchronization of all oscillators cannot be achieved even for sufficiently large values of the coupling strength.