Semi Analytic Solution of Hodgkin-Huxley Model by Homotopy Perturbation Method

摘要

Hodgkin-Huxley model is a system of four non-linear coupleddifferential equations which describes and explains the threshold and action potential by a stimulus arising in a single neuron. The solution andanalysis of Hodgkin-Huxley equations is a formidable task because of thecoupling between non-linear differential equations, lots of unknowns andtheir dependence on many physical parameters. Although this model hasbeen solved by numerical methods, finding an analytic solution is interesting due to the challenges that the continuum model offers. In this paper,first order semi analytic solution of this model, in space-clamped situation,is derived by Homotopy Perturbation Method. We applied this techniquein piece wise manner due to the strong and complex coupling betweenthe variables in the model. Without this modification, finding an accurate analytic solution is impossible for this neural model. Results showthat computed analytic solution has excellent agreement with higher ordernumerical solution. Robustness of the computed analytic solution in different physical scenarios is examined. Further, this analytic solution candescribe many key properties such as the threshold potential, the actionpotential and the refractory period. MATLAB software is used to simulatethe solution.