BURSTING OSCILLATIONS INDUCED BY SMALL NOISE~*

摘要

We consider a model of a square-wave bursting neuron residing in the regime oftonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting.The statistical properties of the emergent bursting patterns are studied in the present work. Inparticular, we identify two principal statistical regimes associated with the noise-induced bursting.In the first case, type I, bursting oscillations are created mainly due to the fluctuations in the fastsubsystem. In the alternative scenario, type II bursting, the random perturbations in the slowdynamics play a dominant role. We propose two classes of randomly perturbed slow-fast systemsthat realize type I and type II scenarios. For these models, we derive the Poincare maps. The analysisof the linearized Poincare maps of the randomly perturbed systems explains the distributions of thenumber of spikes within one burst and reveals their dependence on the small and control parameterspresent in the models. The mathematical analysis of the model problems is complemented by thenumerical experiments with a generic Hodgkin–Huxley-type model of a bursting neuron.