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

Abstract

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