Anti-phase synchronization of waves in a multiplex network of van der Pol oscillators

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-09, Vol.162, p.112447, Article 112447
• Main Authors: Shepelev, I.A., Bukh, A.V., Strelkova, G.I.
• Format: Article
• Language: English
• Subjects: Multiplex networks; Repulsive coupling; Sparse coupling; Spatiotemporal patterns; Spiral wave; Synchronization; Target wave; van der Pol oscillator
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112447

We study numerically the spatiotemporal dynamics and anti-phase synchronization of complex structures in a two-layer multiplex network of bidirectionally and repulsively coupled two-dimensional lattices. Each layer consists of locally and attractively coupled identical van der Pol oscillators. Depending on randomly distributed initial conditions the isolated layers can exhibit either a spiral or a target wave regime. The latter is found for first time for the locally coupled van der Pol lattice considered in this work. We vary the inter-layer coupling strength for either fixed or changing intra-layer coupling strengths in the interacting layers. The numerical results are summarized in the two-dimensional diagrams plotted in the “intra-layer coupling strength – inter-layer coupling strength” parameter plane. Anti-phase synchronization is identified by evaluating the local and global cross-correlation coefficients which are equal to −1. We also explore the impact of random de-multiplexing on the robustness of the observed spatiotemporal structures and anti-phase synchronized regimes in the two-layer network. •Target waves have been found for the first time in a 2D network of locally coupled van der Pol oscillators.•Anti-phase synchronization of wave structures has been shown in a two repulsively coupled 2D lattices.•The robustness of anti-phase synchronization has been explored for sparse inter-layer coupling.