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  1. Ryashko L.B., Slepukhina E.S.
    Analysis of noise-induced bursting in two-dimensional Hindmarsh–Rose model
    Computer Research and Modeling, 2014, v. 6, no. 4, pp. 605-619

    We study the stochastic dynamics of the two-dimensional Hindmarsh–Rose model in the parametrical zone of coexisting stable equilibria and limit cycles. The phenomenon of noise-induced transitions between the attractors is investigated. Under the random disturbances, equilibrium and periodic regimes combine in bursting regime: the system demonstrates an alternation of small fluctuations near the equilibrium with high amplitude oscillations. This effect is analysed using the stochastic sensitivity function technique and a method of estimation of critical values for noise intensity is proposed.

    Keywords: Hindmarsh–Rose model, excitability, stochastic sensitivity, noise-induced transitions, bursting.
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