Strange Nonchaotic Spiking in the Quasiperiodically-forced Hodgkin-Huxley Neuron

초록

We study the transition from a silent state to a spiking state by varying the dc stimulus in the quasiperiodically-forced Hodgkin-Huxley neuron. or Has quasiperiodically-forced case, a new type of strange nonchaotic (SN) spiking state is found to appear between the silent state, and the chaotic spiking state as intermediate one. Using a rational approximation to the quasiperiodic forcing, we investigate the mechanism for the appearance of such an SN spiking state. We thus find that a smooth torus (corresponding to the silent state) is transformed into an SN spiking at:tractor via, a phase-dependent saddle-node bifurcation. This is in contrast; to the periodically-forced case where the silent state transforms directly to a chaotic spiking state. SN spiking states are characterized in terms of the interspike interval, so they are found to be aperiodic complex ones, as in the case of chaotic spiking states. Hence, aperiodic complex spikings may result from two dynamically different; states with strange geometry (one is chaotic and the other one is nonchaotic).

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