| The HH model not only contains the voltage-clamped experimental data but also is remarkably successful in simulating action potential responses, which offers a brilliant future for the quantitative research of excitable physiological nerve character. It explains experimental phenomena accurately and quantitatively analyzes the change of voltages and currents on the nerve cell membrane. Bifurcations have close relations with diseases like Parkinson disease,epilepsy or pathological heart rhythms, etc. To cure such diseases scientists have done many works. Bifurcation control through electrical stimulation is one of them.Bifurcation refers to qualitative changes in the solution structure of dynamical systems occurring with slight variation in system parameters. Bifurcation control means to designning a controller that can modify the bifurcation properties of a given nonlinear system, so as to obtain some desired dynamical behaviors.In this paper we employ the physiological data obtained from rat's muscles voltage-clamped experiments carried by Duva, Adrian and Pappone, and take the Hodgkin-Huxley model for muscles (HHM) as study object. The dynamic bifurcation analysis about single parameter of leakage conductance is performed on the model with the help of algebra criterion in high dimension equations. Based on all these results we choose feedback control methods to stabilize the bifurcation and transform the bifurcation point to another unreachable point. The simulation results verify the validity of such theoretic analysis and control method.At the same time, we took improved HH model as study object and after theoretical analyse and simulation we analyze its phenomenon; then, we choose Washout filter as a controller to stabilize the bifurcation. The easy measureable of membrane voltage make such kind of analyzation a meaningful research.The simulation results verify the analyzation and methods are all correct and can lead a new way toward clinical usage. |
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