Inter-layer synchronization of 2D lattices of van der Pol oscillators with repulsive and attractive intra-layer coupling

Abstract

We for the first time explore numerically the effect of anti-phase synchronization in a heterogeneous two-layer network of two-dimensional (2D) lattices of van der Pol oscillators. The inter-layer coupling of the multiplex network has linear repulsive character. One layer of 2D lattices is characterized by attractive coupling of oscillators and demonstrates a spiral wave regime. The oscillators in the second layer are coupled through active elements and the interaction between them has the repulsive character. We show that the lattice with the repulsive type of coupling demonstrates complex spatiotemporal cluster structures, which can be called as labyrinth-like structures. We show for the first time that this multiplex network with fundamentally different types of intra-layer coupling demonstrates the inter-layer anti-phase synchronization and a competition between two types of structures. Our numerical study indicates that the synchronization threshold and the type of spatiotemporal patterns in both the layers strongly depend on the ratio of the intra-layer coupling strength of the two lattices.

Speaker

Igor A. Shepelev
Saratov State University, 410012, Astrakahskaia str, 83, Saratov
Russia

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