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

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  • Shepelev, I.A.
  • Bukh, A.V.
  • Strelkova, G.I.

Abstract

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.

Suggested Citation

  • Shepelev, I.A. & Bukh, A.V. & Strelkova, G.I., 2022. "Anti-phase synchronization of waves in a multiplex network of van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006579
    DOI: 10.1016/j.chaos.2022.112447
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