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Interplay between solitary states and chimeras in multiplex neural networks

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  • Rybalova, E.V.
  • Zakharova, A.
  • Strelkova, G.I.

Abstract

We study numerically the spatiotemporal dynamics and synchronization of a heterogeneous two-layer multiplex network where each layer is represented by a ring of nonlocally coupled FitzHugh–Nagumo neurons in the oscillatory regime. Being uncoupled, individual layers can show chimera states, solitary states and combined structures (the coexistence of chimera and solitary states) depending on the values of the intralayer coupling parameters and initial conditions. We choose different spatiotemporal patterns in the coupled layers and systematically study synchronization between them when the interlayer coupling is introduced through either the fast (activator) or the slow (inhibitor) variable of the FitzHugh–Nagumo oscillators. Our results enable to uncover the competitive behavior between the solitary states and the chimeras in the transition to synchronous regime in the considered network. We also analyze the synchronization peculiarities for two different types of the interlayer coupling by using the local and global synchronization measures.

Suggested Citation

  • Rybalova, E.V. & Zakharova, A. & Strelkova, G.I., 2021. "Interplay between solitary states and chimeras in multiplex neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003659
    DOI: 10.1016/j.chaos.2021.111011
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    References listed on IDEAS

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    1. 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).
    2. 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.
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    5. 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.
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    8. 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).
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    1. Rybalova, E.V. & Vadivasova, T.E. & Strelkova, G.I. & Zakharova, A., 2022. "Multiplexing noise induces synchronization in multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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