Synchronization of wave structures in a heterogeneous multiplex network of 2D vdP lattices with attractive and repulsive intra-layer coupling

TL;DR

This study numerically investigates how two-layer heterogeneous 2D lattices of van der Pol oscillators with different intra-layer couplings synchronize and form complex patterns, revealing the influence of coupling strength ratios and ranges.

Contribution

It is the first to demonstrate mutual synchronization and structural competition in a multiplex network with contrasting intra-layer couplings.

Findings

Synchronization depends on coupling strength ratio.

Labyrinth-like structures emerge in the repulsively coupled layer.

Synchronization threshold varies with coupling range.

Abstract

We explore numerically the synchronization effects 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 an attractive character. One layer of 2D lattices is characterized by attractive coupling of oscillators and demonstrates a spiral wave regime for both the local and nonlocal interaction. 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 mutual 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. We also analyze the impact of intra-layer coupling ranges on the synchronization effects.