The Modeling Of The Nerve Fiber Stimulated By The Electric Field And Its Nonlinear Analysis

The research on the nerve fiber excitation by electrical stimulation plays an important role in the fields of neuroscience, healing project and so on. It can be divided into two main groups. One is the research on the distribution of the electrical field generated by the electrical stimulation, the other is the modeling of the nerve fiber. In the previous work, more attention was paid on the modeling of the nerve fiber from the biological and mathematical point of view. However, we aim at describing the performance of the system quantitatively and accurately to control the system effectively.In this paper, the nerve fiber is taken as the object for analysis from the view of control theory. Based on the diode model, the first order linear model is analyzed. After introducing the recovery variable into it, the second order linear model is built. Then the frequency response based on the two models are analyzed and compared. Then for the nonlinear performance of the nerve fiber under the super-threshold stimulation, based on the FHN model, the Lurie model of the nerve fiber is built. The stability of the system is analyzed, and the conclusion is drawn that the system is asymptotic stable and the convergent velocity is related with the electrical property of the nerve fiber. Based on the revised theorem for the Lurie system, the nonlinear system of the nerve fiber is proved theoretically to be input-output stable. Furthermore, the response of the nerve fiber in the uniform electrical field is analyzed. The theoretical conclusions are proved by the simulation results.