Estimate the electrical activity in a neuron under depolarization field

Abstract The physical electric variable is included into the known Hindmarsh-Rose (HR) model for estimating the depolarization field effect and then external current forcing is applied to detect the firing responses. Based on the proposed model, the effects of the amplitude and frequency of the sinusoidal current on the firing mode of the neuron are studied by using bifurcation analysis. It is found that there is a peak of firing interval of neurons with the increasing of stimulation current intensity. In the presence of electric field, the firing pattern of neuron is transformed from single busting to intermittent multimodal busting with the increasing of frequency and amplitude of electric field. The largest Lyapunov exponent is drawn for verification. In the absence of electric field, the two neurons coupled in the first variable achieve synchronization in busting mode. If there is an external electric field, the two neurons can achieve intermittent multimodal busting firing synchronization even without direct variable couple since the energy is injected into the coupled system by the external electric field. Our results show that the periodic external electric field and external current stimulation play an important role in the neuronal firing pattern.