Unified mechanism of inverse stochastic resonance for monostability and bistability in Hindmarsh-Rose neuron.

Noise is ubiquitous and has been verified to play constructive roles in various systems, among which the inverse stochastic resonance (ISR) has aroused much attention in contrast to positive effects such as stochastic resonance. The ISR has been observed in both bistable and monostable systems for which the mechanisms are revealed as noise-induced biased switching and noise-enhanced stability, respectively. In this paper, we investigate the ISR phenomenon in the monostable and bistable Hindmarsh-Rose neurons within a unified framework of large deviation theory. The critical noise strengths for both cases can be obtained by matching the timescales between noise-induced boundary crossing and the limit cycle. Furthermore, different stages of ISR are revealed by the bursting frequency distribution, where the gradual increase of the peak bursting frequency can also be explained within the same framework. The perspective and results in this paper may shed some light on the understanding of the noise-induced complex phenomena in stochastic dynamical systems.