BVP models: An adjustment to express a mechanism of inactivation

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Abstract
Fitzhugh's BVP model has been used by many people. Fitzhugh has pointed out that as the stimulus is increased the model has “inverted” behaviour. It is here shown that this is due to a lack of a mechanism of inactivation, and the model is adjusted by supplying such a mechanism, to give a new model, called BPH, which, like Fitzhugh's, is of second order, with one equation of first degree and the other of third degree in the dynamical variables. Numerical solutions of the new system are compared with numerical solutions of the Hodgkin-Huxley and of the Fitzhugh equations.