The Hopf Bifurcation of a Neuron Model

The theory of nonlinear dynamical system was used to describe the phenomenon of neural rest and spikes. It is shown that the quiescent state of neuron is mathematically equivalent to a stable spiral, the neural excitability is referred to a state near bifurcation, and the periodic spike is equivalent to a stable limit cycle in the Hopf bifurcation. Similarly, the phenomenon of restrain after too strong an excitation corresponds to the second Hopf bifurcation.