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

Abstract

The paper describes the effects of mutual and external synchronization of spiral wave structures in two coupled two-dimensional lattices of coupled discrete-time oscillators. Each lattice is given by a 2D N×N network of nonlocally coupled Nekorkin maps which model neuronal activity. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of the synchronization scenario. 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.