Analysis of noise-induced transitions between spiking and bursting regimes in Hindmarsh–Rose neuron model

The stochastic dynamics of the Hindmarsh–Rose model of neuronal activity is studied. For the parametric zone of tonic spiking oscillations, it is shown that random disturbances transform the spiking dynamic regime into the bursting one. For a quantitative analysis of the noiseinduced bursting, we suggest a constructive approach based on the stochastic sensitivity function technique and the method of confidence domains. It allows us to give a geometric description for a distribution of random states around the deterministic attractors and estimate critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in a good agreement with direct numerical simulations.