Resonance in a model of a mammalian neuron.

In this paper we show that for a small range of voltages the model described in the previous paper (Hindmarsh & Rose Phil. Trans. R. Soc. Lond. B 346, 129-150 (1994a)) will generate damped oscillations in response to a negative current pulse. As a consequence the cell has the property that it can be driven into bursting by periodic sinusoidal inputs close to the resonant frequency. The main objective of this paper is to analyse this resonant behaviour using the model of the model introduced in the previous paper. We derive analytical expressions which closely approximate the nonlinear resonance observed in the physiological model driven by a periodic sinusoidal input. This leads to the conclusion that resonance could play a role in synaptic transmission at relay nuclei in the mammalian brain.