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Transformations of spike and burst oscillations in the stochastic Rulkov model

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  • Bashkirtseva, Irina
  • Ryashko, Lev

Abstract

We study the problem of modeling and analysis of complex oscillatory regimes in neuron dynamics on the basis of the two-dimensional Rulkov model. We focus on the parameter zone in which sharp changes in the type of oscillatory activity occur: burst oscillations with an active phase of a triangular shape are transformed into bimodal bursts combining triangular and trapezoidal phases. Mechanisms of such transformations are clarified geometrically by the technique of critical curves. For the stochastically forced model, we study two phenomena: (i) noise-induced splitting of tonic spiking; (ii) noise-induced transitions from the triangular mono-bursting to the more complicated bi-bursting. The phenomena of coherence and anti-coherence resonance are revealed and discussed.

Suggested Citation

  • Bashkirtseva, Irina & Ryashko, Lev, 2023. "Transformations of spike and burst oscillations in the stochastic Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923003156
    DOI: 10.1016/j.chaos.2023.113414
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    References listed on IDEAS

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    1. D. Valenti & G. Augello & B. Spagnolo, 2008. "Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 443-451, October.
    2. Bashkirtseva, Irina & Ryashko, Lev, 2022. "Stochastic generation and shifts of phantom attractors in the 2D Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Bashkirtseva, Irina & Nasyrova, Venera & Ryashko, Lev, 2018. "Noise-induced bursting and chaos in the two-dimensional Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 76-81.
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