Stochastic Generation and Deformation of Toroidal Oscillations in Neuron Model

Abstract

The stochastic Hindmarsh–Rose neuron model in the parametric regions of complex nonlinear dynamics with quiescent and torus bursting regimes is studied. We show that in the zone where the deterministic system exhibits the quiescence, noise can lead to the generation of toroidal dynamical structure with the transition to the bursting regime. The studies of dispersion of random trajectories as well as power spectral density and interspike intervals distribution confirm these changes in system dynamics. Moreover, the stochastic emergence of torus is followed by the noise-induced chaotization. We show that the generation of the torus bursting oscillations is associated with the specificity of the arrangement of deterministic trajectories in the vicinity of the equilibrium as well as its stochastic sensitivity. A probabilistic mechanism of the stochastic generation of torus is investigated on the basis of the analysis of the stochastic sensitivity and geometry of confidence regions. We also show that in the parametric range of the torus bursting, noise can lead to the increase of number of bursts per time interval and to the reduction of spiking and quiescent phase duration.