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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
In this paper, the partial differential equation for wave propagation of an axon under stochastic noises is given and then simplified to the ordinary differential equation for the traveling wave with constant velocity by using the traveling wave coordinate. The stochastic wave solution is divided into a deterministic part and its stochastic perturbation. A deterministic traveling wave solution for the action potential is obtained by solving the nonlinear wave equation without stochastic excitation. The nonlinear wave equation with stochastic excitation for the stochastic perturbation is transformed into the It? stochastic differential equations. The corresponding Fokker-Planck-Kolmogorov equation is given, and then the probability density and statistics of the stochastic wave perturbation are obtained. The stability of the stochastic wave propagation in the nonlinear model from the axon is analyzed and illustrated with numerical results.
Keywords:stochastic noise; nonlinear wave; instability; probability density