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Noise-induced chaos and generation of phantom attractors in a birhythmic neuron model

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  • Ryashko, Lev
  • Bashkirtseva, Irina

Abstract

We analyze mechanisms of stochastic transformations of complex oscillatory regimes in the 2D Rulkov model with the smooth map. In the birhythmicity parametric zone with coexistence of periodic and chaotic oscillations, noise-induced transitions from regular spiking to chaotic bursting are studied. In the monorhythmicity zone of regular periodic oscillations, the stochastic phenomenon of the systematic shift of probability distributions with generation of a phantom chaotic attractor is discovered and analyzed. The relationship of this phenomenon with the presence of transient chaotic attractors in the original deterministic model is revealed and discussed. For parametric analysis of these phenomena, we apply the confidence ellipses method based on the stochastic sensitivity technique.

Suggested Citation

  • Ryashko, Lev & Bashkirtseva, Irina, 2025. "Noise-induced chaos and generation of phantom attractors in a birhythmic neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013936
    DOI: 10.1016/j.chaos.2024.115841
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    References listed on IDEAS

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    1. Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    3. Bashkirtseva, Irina & Ryashko, Lev, 2022. "Stochastic generation and shifts of phantom attractors in the 2D Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. I.B., Tagne nkounga & F.M., Moukam kakmeni & R., Yamapi, 2022. "Birhythmic oscillations and global stability analysis of a conductance-based neuronal model under ion channel fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Bashkirtseva, I. & Ryashko, L., 2024. "Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
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