PERIODIC AND NON-PERIODIC RESPONSES OF A PERIODICALLY FORCED HODGKIN-HUXLEY OSCILLATOR

Membrane potential responses of a Hodgkin-Huxley oscillator to an externally-applied sinusoidal current were numerically calculated with relation to bifurcation parameters of the amplitude and the frequency of the stimulating current. The Hodgkin-Huxley oscillator, or the Hodgkin-Huxley axon in the state of self-sustained oscillation of action potentials, was realized by immersing the axon in Ca-deficient sea water. The forced oscillations were analyzed by the stroboscopic plots and/or the Lorenz plots. The periodically forced Hodgkin-Huxley oscillator exhibits not only periodic motions (harmonic or sub-harmonic synchronization) but also non-periodic motions (quasi-periodic or chaotic oscillation), that the motions were determined by the amplitude and the frequency of the stimulating current, and that the characteristic motions obtained were in reasonable agreement with those of previous results, found experimentally in squid giant axons. Two kinds of route to the chaotic oscillations were found: successive period-doubling bifurcations and formation of the intermittently chaotic oscillation from sub-harmonic synchronization.