Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise

Abstract

We describe general characteristics of the Hodgkin-Huxley neuron's response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude $I_0$ and scales as $(I_0-I_{th})^{1/2}$, where $I_{th}$ is an approximate threshold. Intervals of continuous irregular response alternate with integer mode-locked regions with bistable excitation edge. There is an even-all multimodal transition between the 2:1 and 3:1 states in the vicinity of the main resonance, which is analogous to the odd-all transition discovered earlier in the high-frequency regime. For $I_0<I_{th}$ and small noise the firing rate has a maximum at the resonant frequency. For larger noise and subthreshold stimulation the maximum firing rate initially shifts towards lower frequencies, then returns to higher frequencies in the limit of large noise. The stochastic coherence antiresonance, defined as the maximum of the coefficient of variation as a function of noise intensity, occurs over a wide range of parameter values, including monostable regions.