Abstract: 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.