Bona-fide stochastic resonance in the stochastic FitzHugh-Nagumo neuron

Abstract

The phenomena of stochastic resonance (SR) have attracted much attention in studies of excitable systems, in particular the nervous systems, under noise. Recently, an alternative SR, condition, called bona-fide SR, was proposed in a bistable system, based on the notion of residence time distribution. As the forcing frequency increased, the existence of a resonant frequency was observed. We study SR in a stochastic FitzHugh-Nagumo (FHN) neuron, and we find bona-fide stochastic resonance, the resonance between the forcing frequency and stochastic time scale. The bona-fide stochastic resonance for the FitzHugh-Nagumo neuron is understood through analysis of the phase portraits. The analysis of the phase portraits reveals that it is due to the fact that in the case of the FitzHugh-Nagumo neuron the loop enters the stable state region. An order parameter is introduced to measure the averaged phase synchronization between the sinusoidal input current and the neural responses, which also shows bona-fide stochastic resonance at nearly the same frequency as those observed in inter-spike interval histogram (ISIH) analysis.