Strange responses to fluctuating inputs in the hindmarsh-rose neurons

A Input-Output relationship of a neuron is often used to characterize the function of the neuron. In that case, inputs are assumed to be constant, and neuronal responses to fluctuated inputs are less understood. A recent work reported a strange response of the Hodgkin-Huxley neuron to the fluctuated inputs that an irregularity of spike trains is inversely proportional to an input irregularity. In this paper, we investigated an origin of the strange response by using the Hindmarsh-Rose neuron. We provided the parameter regions for bifurcations and confirmed that the Hindmarsh-Rose neuron reproduces the strange response in dynamics of Saddle-Node and Subcritical Hopf bifurcations. In both bifurcation cases, the Hindmarsh-Rose neuron shows a bistability of resting potential and repetitive firing. This indicates that the bistability is the origin of the strange input-output relationship.