Bistability in Hodgkin-Huxley-type equations

Abstract

We study how initial conditions of the Hodgkin-Huxley model affect the dynamics of simulated neurons. We systematically vary the amplitudes of depolarization currents in order to bring neuron dynamics to stable equilibrium. Our results demonstrate that simulated neurons can have spontaneous spiking or a silent state, depending on the initial conditions. We propose the methodology to study the circumstances under which Purkinje cells transit between hyperpolarized quiescent state (down state) and a depolarized spiking state (up state). We show that results derived using the Hodgkin-Huxley methodology should be carefully analyzed before suggesting a direct relevance to neuroprosthetic implants..