An Analysis of Neuron Excitation Dynamics for Gaussian Noises

The study of role of noises in the neural systems has recently become an interesting subject. The models in practical use for neuron excitation are simple and can not show exact response for the inputs with noises. Hodzkin and Huxley proposed an excellent mathematical model describing the dynamics of excitation of the neural cell. This model with the higher order differential equations, however, is difficult to handle in the practical use.In this paper, the dynamics of neuron excitation for Gaussian noises were analyzed by using Hodzkin-Huxley equation in detail. From the calculated analysis the followings were proved. The probability of excitation decreased with deviation of membrane current density (σ). The frequency of limit cycle produced by excitation are constant and not related to σ. The deviations of membrane potential(V) increased with σ in the stable or non excitation regions. The probability distribution of V can be calculated by the Fokker-Planck equation.