Pararrieter dependence of a bona-fide stochastic resonance in a stochastic FitzHugh-Nagumo neuron

Recently, an alternative stochastic resonance (SR) condition, called the bona-fide SR, was proposed for a bistable system based on the notions of a residence time distribution, and the existence and the structure of optimal resonant frequencies with maximal resonances at a given noise intensity are investigated actively in various systems. In this paper, the bona-fide stochastic resonance is studied in the stochastic FitzHugh-Nagumo neuron, focusing on the dependence of optimal resonant frequencies on the noise intensity, especially, at small noise intensity. Interestingly, the resonant frequencies become non-zero constant values when the noise intensity becomes very small, which is qualitatively different from the bistable system where the resonant frequency goes to zero at small noise intensity. In fact, these nonzero resonant frequencies corresponding to forcing frequencies with minimal amplitudes in the mode-locking states of the deterministic condition; and this correspondency is discussed with the notion of a noise-induced transition. The contours of the order parameters also show functional shape that are very similar to the phase boundaries of mode-locking states. These observations provide a clear relationship between the bona-fide SR and the phase boundaries of mode-locking states.