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Mechanism of realizing a solitary state chimera in a ring of nonlocally coupled chaotic maps

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  • Rybalova, E.V.
  • Strelkova, G.I.
  • Anishchenko, V.S.

Abstract

We study the mechanism of appearance of a solitary state chimera in a ring of nonlocally coupled two-dimensional chaotic maps. We show that both solitary states and the solitary state chimera can be induced by noise which multiplicatively modulates the nonlocal coupling coefficient in the ensemble of nonlocally coupled Henon maps. It is demonstrated that these states can also arise due to multistability in the network. It has been firstly shown and explained the possibility of obtaining the solitary states and the solitary state chimera in the one-dimensional ring of nonlocally coupled Henon maps. Basins of attraction of coexisting attractors essentially depend on the spatiotemporal structure, which is realized in the ring, as well as on the position of a particular oscillator among the other oscillators. We have found out that the riddling effect of the basins of attraction can be observed when the network state shows an amplitude chimera.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:300-305
    DOI: 10.1016/j.chaos.2018.09.003
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    Cited by:

    1. Lazarides, N. & Hizanidis, J. & Tsironis, G.P., 2020. "Controlled generation of chimera states in SQUID metasurfaces using DC flux gradients," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. 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).
    3. 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).
    4. A.V., Bukh & V.S., Anishchenko, 2020. "Spiral and target wave chimeras in a 2D network of nonlocally coupled van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. 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).
    6. Rybalova, E. & Averyanov, V. & Lozi, R. & Strelkova, G., 2024. "Peculiarities of the spatio-temporal dynamics of a Hénon–Lozi map network in the presence of Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    7. 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).
    8. 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).

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