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Unstable Propagation in a Stochastic Nonlinear Wave Model from an Axon
YING Zuguang * #
Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
*Correspondence author
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Funding: none
Opened online:21 April 2015
Accepted by: none
Citation: YING Zuguang.Unstable Propagation in a Stochastic Nonlinear Wave Model from an Axon[OL]. [21 April 2015] http://en.paper.edu.cn/en_releasepaper/content/4638772
 
 
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
 
 
 

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