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 transitionsbetween the attractors is investigated. Under the random disturbances, equilibrium and periodic regimes combinein bursting regime: the system demonstrates an alternation of small fluctuations near the equilibrium with highamplitude oscillations. This effect is analysed using the stochastic sensitivity function technique and a methodof estimation of critical values for noise intensity is proposed.