A theoretical description of inverse stochastic resonance in nature

The inverse stochastic resonance (ISR) phenomenon consists of an unexpected depression in the response of a system under external noise, e.g., as observed in the mean firing rate in some pacemaker neurons subject to moderate values of noise. A possible cause for such unexpected reaction is the occurrence of a bistable regime controlling these neurons dynamics. We here explore theoretically the emergence of ISR in a general bistable model system, and thus determine the specific conditions the potential function driving the dynamics must accomplish. We conclude 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 having a larger basin of attraction than the low activity state which is the global minimum of the system. We then discuss on the relevance of such a picture to understand the ISR features and to predict its appearance in nature. In addition, we report on existence of another intriguing, non-standard stochastic resonance in our model even in the absence of any weak signal input. Depending on the shape of the potential function, this new phenomenon shows up together with ISR precisely within the theoretical framework we present in this paper. © 2019 Elsevier B.V.Ministry of Education, Science and Technology Agencia Estatal de Investigación: FIS2017-84256-P Federación Española de Enfermedades RarasWe acknowledge the Spanish Ministry for Science and Technology and the “Agencia Española de Investigación” ( AEI ) for financial support under grant FIS2017-84256-P (FEDER funds). We also thank fruitful comments from P. L. Garrido