Analysis of noise-induced bursting in two-dimensional Hindmarsh–Rose model

Ryashko L.B., Slepukhina E.S.
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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
Citation in English: Ryashko L.B., Slepukhina E.S. Analysis of noise-induced bursting in two-dimensional Hindmarsh–Rose model // Computer Research and Modeling, 2014, vol. 6, no. 4, pp. 605-619
Citation in English: Ryashko L.B., Slepukhina E.S. Analysis of noise-induced bursting in two-dimensional Hindmarsh–Rose model // Computer Research and Modeling, 2014, vol. 6, no. 4, pp. 605-619
DOI: 10.20537/2076-7633-2014-6-4-605-619
URL: http://crm-en.ics.org.ru/journal/article/2171/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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