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Noise-induced bursting and chaos in the two-dimensional Rulkov model

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  • Bashkirtseva, Irina
  • Nasyrova, Venera
  • Ryashko, Lev

Abstract

We study an effect of random disturbances on the discrete two-dimensional Rulkov neuron model. We show that close to the Neimark–Sacker bifurcation, the increasing noise can cause the transition from the noisy quiescence with small-amplitude oscillations near the stable equilibria to the stochastic bursting with large-amplitude spikes. Mean values and variations of the interspike intervals are studied in dependence of the noise intensity. To study the noise-induced bursting, the analytical approach based on the stochastic sensitivity functions technique and confidence ellipses method is applied. On the basis of the largest Lyapunov exponents, we show how the noise-induced transition from the quiescence to stochastic bursting regime is accompanied by the transformation of dynamics from regular to chaotic.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:76-81
    DOI: 10.1016/j.chaos.2018.03.011
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    References listed on IDEAS

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    1. Franović, Igor & Miljković, Vladimir, 2011. "Functional motifs: a novel perspective on burst synchronization and regularization of neurons coupled via delayed inhibitory synapses," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 122-130.
    2. Che, Yan-Qiu & Wang, Jiang & Si, Wen-Jie & Fei, Xiang-Yang, 2009. "Phase-locking and chaos in a silent Hodgkin–Huxley neuron exposed to sinusoidal electric field," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 454-462.
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    Cited by:

    1. Bashkirtseva, I. & Ryashko, L., 2019. "Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 78-84.
    2. Bashkirtseva, Irina A. & Ryashko, Lev B. & Pisarchik, Alexander N., 2020. "Ring of map-based neural oscillators: From order to chaos and back," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Bashkirtseva, Irina & Ryashko, Lev, 2023. "Transformations of spike and burst oscillations in the stochastic Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Bashkirtseva, Irina & Zaitseva, Svetlana, 2021. "Variability, transients and excitement in a stochastic model of enzyme kinetics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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