Abstract
The bifurcation theory involves qualitative analysis of variations in singular and certain periodic solutions of differential equations representing a dynamic system. The model proposed by Hodgkin and Huxley for nerve membrane dynamics illustrates certain concepts from this theory. The membrane current, Im is shown to be the bifurcation parameter. At certain values of this parameter, namely at bifurcation values, the character and the stability properties of singular solutions and the other limiting sets such as limit cycles change as predicted by the theory.
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