Abstract
A qualitative mathematical model of Hodgkin-Huxley current clamped system is deduced on the base of fundamental electrodynamic laws of charge and energy conservation. The presence of feedback in the considered system is expressed by physically wellgrounded dependence of the dissipative characteristics (electric resistance) on the state. By this way, an essential nonlinearity is introduced to the system of two differential equations describing the behavior of the modeled excitable system. It is shown by stability and bifurcation theory analysis this behavior (excitability) can be characterized as follows: under an external current disturbance a phase reconstruction (bifurcation) occurs from stable to unstable steady state around which selfoscillations of the excitable membrane potential and transmembrane ion current emerge. After removing of the disturbance, an inverse phase reconstruction is observed during which the selfoscillations disappear and the unstable steady-state values of the potential and current become stable.
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