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Solitary states in multiplex neural networks: Onset and vulnerability

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  • Schülen, Leonhard
  • Janzen, David A.
  • Medeiros, Everton S.
  • Zakharova, Anna

Abstract

We investigate solitary states in a two-layer multiplex network of FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary states can be induced in a multiplex network consisting of two non-identical layers. More specifically, we show that these patterns can be introduced via weak multiplexing into a network that is fully synchronized in isolation. We show that this result is robust under variations of the inter-layer coupling strength and largely independent of the choice of initial conditions. Moreover, we study the vulnerability of solitary states with respect to changes in the inter-layer topology. In more detail, we remove links that connect two solitary nodes of each layer and evaluate the resulting pattern. We find a highly non-trivial dependence of the survivability of the solitary states on topological (position in the network) and dynamical (phase of the oscillation) characteristics.

Suggested Citation

  • Schülen, Leonhard & Janzen, David A. & Medeiros, Everton S. & Zakharova, Anna, 2021. "Solitary states in multiplex neural networks: Onset and vulnerability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921000230
    DOI: 10.1016/j.chaos.2021.110670
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    References listed on IDEAS

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    1. Schülen, Leonhard & Ghosh, Saptarshi & Kachhvah, Ajay Deep & Zakharova, Anna & Jalan, Sarika, 2019. "Delay engineered solitary states in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 290-296.
    2. Shepelev, I.A. & Bukh, A.V. & Muni, S.S. & Anishchenko, V.S., 2020. "Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Jakub Sawicki & Iryna Omelchenko & Anna Zakharova & Eckehard Schöll, 2019. "Delay-induced chimeras in neural networks with fractal topology," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(3), pages 1-8, March.
    4. Rybalova, E.V. & Strelkova, G.I. & Anishchenko, V.S., 2018. "Mechanism of realizing a solitary state chimera in a ring of nonlocally coupled chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 300-305.
    5. Frank Hellmann & Paul Schultz & Patrycja Jaros & Roman Levchenko & Tomasz Kapitaniak & Jürgen Kurths & Yuri Maistrenko, 2020. "Network-induced multistability through lossy coupling and exotic solitary states," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    6. 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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