The bifurcation behaviour of a novel second order model of the Hodgkin-Huxley Neuron

A novel second order neuron is presented which exhibits the principal bifurcations observed in the Hodgkin-Huxley (HH) neuron. The new model is based on the topological normal form for the Bautin bifurcation. The effect of electrical coupling on the local dynamics of the equilibrium of two coupled second order neurons is shown to be similar to the effect of coupling on the local dynamics of the equilibrium of two coupled HH neurons. In particular, the equilibriums of both types of coupled neurons experience a Hopf bifurcation as the coupling parameter is increased from zero.