Oscillatory activity induced by noise in Hodgkin-Huxley-type of model with stable steady state

The dynamics of the Hodgkin-Huxley –type of model is considered. The Transition from bistable to monostable dynamics is described via a boundary crisis of the bursting attractor. We consider the influence of noise on the dynamics of the Hodgkin-Huxley-type model. It is shown that for a single stable equilibrium, noise can induce oscillatory activity of the spiking-type and the bursting-type.