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Coexisting Attractors and Multistate Noise-Induced Intermittency in a Cycle Ring of Rulkov Neurons

Author

Listed:
  • Irina A. Bashkirtseva

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

  • Alexander N. Pisarchik

    (Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, Pozuelo de Alarcón, 28223 Madrid, Spain)

  • Lev B. Ryashko

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

Abstract

We study dynamics of a unidirectional ring of three Rulkov neurons coupled by chemical synapses. We consider both deterministic and stochastic models. In the deterministic case, the neural dynamics transforms from a stable equilibrium into complex oscillatory regimes (periodic or chaotic) when the coupling strength is increased. The coexistence of complete synchronization, phase synchronization, and partial synchronization is observed. In the partial synchronization state either two neurons are synchronized and the third is in antiphase, or more complex combinations of synchronous and asynchronous interaction occur. In the stochastic model, we observe noise-induced destruction of complete synchronization leading to multistate intermittency between synchronous and asynchronous modes. We show that even small noise can transform the system from the regime of regular complete synchronization into the regime of asynchronous chaotic oscillations.

Suggested Citation

  • Irina A. Bashkirtseva & Alexander N. Pisarchik & Lev B. Ryashko, 2023. "Coexisting Attractors and Multistate Noise-Induced Intermittency in a Cycle Ring of Rulkov Neurons," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:597-:d:1045133
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    References listed on IDEAS

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    1. Andreev, Andrey V. & Maksimenko, Vladimir A. & Pisarchik, Alexander N. & Hramov, Alexander E., 2021. "Synchronization of interacted spiking neuronal networks with inhibitory coupling," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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