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Dynamics of non–identical coupled Chialvo neuron maps

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  • Kuznetsov, A.P.
  • Sedova, Y.V.
  • Stankevich, N.V.

Abstract

We study numerically the dynamics of low–dimensional ensembles of discrete neuron models - Chialvo maps. We are focused on choosing the autonomous map parameters corresponding to the invariant curve. We consider two cases of coupling organization: (i) via a nonlinear function of models; (ii) linear coupling, which is an analog of electrical neuron interaction. For the first case, the possibility of invariant curve doublings and the emergence of quasi-periodicity within Arnold tongues as a result of the secondary Neimark-Sacker bifurcation are found. For the second case, we discover an area of three-frequency quasi-periodicity for the case of two neurons. It arises softly as a result of quasi-periodic Hopf bifurcation. We demonstrate a set of resonant two-frequency regimes tongues embedded in this area and bounded by lines of saddle-node bifurcations of invariant curves. For ensemble of three linearly coupled maps, four-frequency quasi-periodicity becomes possible with a built-in system of tongues of three-frequency regimes (tori). We discuss the effect of noise and the evolution of “noise quasi-periodic” regimes, resonant regimes of this type and bifurcations of invariant tori with increasing of noise intensity.

Suggested Citation

  • Kuznetsov, A.P. & Sedova, Y.V. & Stankevich, N.V., 2024. "Dynamics of non–identical coupled Chialvo neuron maps," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007896
    DOI: 10.1016/j.chaos.2024.115237
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    References listed on IDEAS

    as
    1. Kuznetsov, Alexander P. & Kuznetsov, Sergey P. & Sedova, Julia V., 2006. "Effect of noise on the critical golden-mean quasiperiodic dynamics in the circle map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 48-64.
    2. Beims, Marcus W. & Rech, Paulo C. & Gallas, Jason A.C., 2001. "Fractal and riddled basins: arithmetic signatures in the parameter space of two coupled quadratic maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 276-279.
    3. dos Santos, Vagner & Szezech Jr., José D. & Baptista, Murilo S. & Batista, Antonio M. & Caldas, Iberê L., 2016. "Unstable dimension variability structure in the parameter space of coupled Hénon maps," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 23-28.
    4. Stankevich, N.V. & Gonchenko, A.S. & Popova, E.S. & Gonchenko, S.V., 2023. "Complex dynamics of the simplest neuron model: Singular chaotic Shilnikov attractor as specific oscillatory neuron activity," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Used, Javier & Seoane, Jesús M. & Bashkirtseva, Irina & Ryashko, Lev & Sanjuán, Miguel A.F., 2024. "Synchronization of two non-identical Chialvo neurons," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    7. Rech, Paulo C. & Beims, Marcus W. & Gallas, Jason A.C., 2004. "Naimark–Sacker bifurcations in linearly coupled quadratic maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 351-355.
    8. Muni, Sishu Shankar & Rajagopal, Karthikeyan & Karthikeyan, Anitha & Arun, Sundaram, 2022. "Discrete hybrid Izhikevich neuron model: Nodal and network behaviours considering electromagnetic flux coupling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
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