Theory for Inverse Stochastic Resonance in Nature

The inverse stochastic resonance (ISR) phenomenon consists in an unexpected depression in the response of a system under external noise, e.g., as observed in the behavior of the mean-firing rate in some pacemaker neurons in the presence of moderate values of noise. A possible requirement for such behavior is the existence of a bistable regime in the behavior of these neurons. We here explore theoretically the possible emergence of this behavior in a general bistable system, and conclude on conditions the potential function which drives the dynamics must accomplish. We show that such an intriguing, and apparently widely observed, phenomenon ensues in the case of an asymmetric potential function when the high activity minimum state of the system is metastable with the largest basin of attraction and the low activity state is the global minimum with a smaller basin of attraction. We discuss on the relevance of such a picture to understand the ISR features and to predict its general appearance in other natural systems that share the requirements described here. Finally, we report another intriguing non-standard stochastic resonance in our system, which occurs in the absence of any weak signal input into the system and whose emergence can be explained, with the ISR, within our theoretical framework in this paper in terms of the shape of the potential function.