Anti-phase relay synchronization of wave structures in a heterogeneous multiplex network of 2D lattices

• Published in: Chaos, solitons and fractals Vol. 143; p. 110545
• Main Authors: Shepelev, I.A., Bukh, A.V., Strelkova, G.I., Anishchenko, V.S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2021
• Subjects: 2D Lattice; Chimera; Multiplex networks; Nonlocal coupling; Spatiotemporal patterns; Spiral wave; Synchronization; Target wave chimera; Spatiotemporal patterns; Nonlocal coupling; Target wave chimera; Multiplex networks; Spiral wave; 2D Lattice; Synchronization; Chimera
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110545

•Anti-phase relay synchronization is established for the first time in a triplex network of 2D lattices.•The correlation coefficient measure is used for the first time as a relay synchronization criterion.•Strong inter-layer coupling induces in-phase complete synchronization. We explore numerically relay synchronization of wave structures in a heterogeneous three-layer network of coupled two-dimensional (2D) lattices of continuous-time systems. Remote layers, which are not directly connected but interact via a relay layer, consist of coupled van der Pol oscillators, while the middle layer is described by a lattice of interacting FitzHugh-Nagumo neurons. We show for the first time that already for weak inter-layer coupling, anti-phase relay synchronization of target wave patterns occurs in the considered network. This is a novel effect which can be observed in multiplex networks of interacting 2D lattices of oscillatory systems. Our numerical studies indicate that strong inter-layer coupling leads to in-phase synchronization of spatio-coherent structures in the network layers. We also analyze the impact of inter-layer coupling ranges in the relay and the remote layers on the relay synchronization effect.