  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.
