ABSTRACT
The Bonhoeffer–van der Pol (BVP) or the FitzHugh–Nagumo (FHN) neuronal model is well known to be a simplified and a tractable model of the Hodgkin-Huxley (HH) model, and preserves several neuronal properties such as an excitability, a refractoriness, a repetitive activity by an external current. This chapter presents the BVP neuronal model and briefly explains the neuronal feature (excitability, refractoriness, repetitive activity, etc.) of the model. It considers the model in the (singular) limit of a parameter and studies the effects of a sinusoidal input on the singular model. The effects of the asymmetry of the model on the bifurcation structures are also analyzed. If the period of the sinusoidal input is long, then the BVP neuron model produces a bursting oscillation, in which an active phase with successive spikes and a silent phase without spikes alternate.
