On a response characterictics in the Hodgkin-Huxley model of nerve and muscle fiber to a periodic stimulation

For nerve anon the Hodgkin-Huxley equations, H-H equations or H-H model for short, shows the chaotic response under the periodic electrical stimulous. For muscle filer, Falk and Fatt formulated the Falk Fatt equations (the F-F equations or F-F model) which are nonlinear equations similar to those of Hodgkin and Huxley. However, the response characteristics of the model has not been studied in detail. In the present study, several aspects of the H-H model and the F-F modelis studied. The H-H model and F-F model are solved with a periodic stimulation (Acos omegat, omega = 2pif). The Chaotic responses are observed under a special condition on an amplitude and frequency. The production procedure of a chaotic response is investigated. In order to investigate the general characteristics of the H-H model and F-F model are average firing rate is computed;and phase variables are drawn in phase plane. Finally,the relationship between the F-F model and the H-H model is considered. For the same periodic stimulation, the F-F model shows the chaotic response and the H-H model shows the n/m phase-locked oscilation or vice vrsa.