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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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    1. Laurent Larger & Bogdan Penkovsky & Yuri Maistrenko, 2015. "Laser chimeras as a paradigm for multistable patterns in complex systems," Nature Communications, Nature, vol. 6(1), pages 1-7, November.
    2. Louis M. Pecora & Francesco Sorrentino & Aaron M. Hagerstrom & Thomas E. Murphy & Rajarshi Roy, 2014. "Cluster synchronization and isolated desynchronization in complex networks with symmetries," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    3. Peter J. Menck & Jobst Heitzig & Jürgen Kurths & Hans Joachim Schellnhuber, 2014. "How dead ends undermine power grid stability," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    4. Rybalova, E.V. & Strelkova, G.I. & Anishchenko, V.S., 2021. "Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Marcel Salathé & James H Jones, 2010. "Dynamics and Control of Diseases in Networks with Community Structure," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-11, April.
    6. Sunghoon Hong & Youngsub Chun, 2010. "Efficiency and stability in a model of wireless communication networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 441-454, March.
    7. Shepelev, I.A. & Bukh, A.V. & Strelkova, G.I. & Anishchenko, V.S., 2021. "Anti-phase relay synchronization of wave structures in a heterogeneous multiplex network of 2D lattices," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Ghosh, Saptarshi & Zakharova, Anna & Jalan, Sarika, 2018. "Non-identical multiplexing promotes chimera states," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 56-60.
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