Shinji Doi

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We have presented a new generation mechanism of slow spiking or repetitive discharges with extraordinarily long inter-spike intervals using the modified Hodgkin-Huxley equations (Doi and Kumagai, 2001). This generation process of slow firing is completely different from that of the well-known potassium A-current in that the steady-state current-voltage(More)
The Hodgkin-Huxley equations with a slight modification are investigated, in which the inactivation process (h) of sodium channels or the activation process of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau potential, such as in heart muscle cells, to chaotic bursting(More)
The Hodgkin-Huxley (HH) equations with a modification in which the inactivation process (h variable) of sodium channels is slightly slowed down are investigated. It is shown that this slight modification changes the HH dynamics to a completely different one, with chaotic spiking and very long interspike intervals appearing in a generic manner, although the(More)
The Hodgkin-Huxley equations (HH) are parameterized by a number of parameters and shows a variety of qualitatively different behaviors depending on the parameter values. We explored the dynamics of the HH for a wide range of parameter values in the multiple-parameter space, that is, we examined the global structure of bifurcations of the HH. Results are(More)
The characteristics of the BVP neuron model response to periodic pulse stimuli are investigated. Temporal patterns of the output of the model are analyzed as a function of the stimulus intensity and period. The BVP model exhibits the same chaotic behavior, and a Cantor function-like graph of the response frequency (mean firing rate) as in(More)
The response characteristics of the BVP (Bonhoeffer-van der Pol or FitzHugh-Nagumo) neuronal model to periodic pulse trains were investigated. The global bifurcation structure of model relative to stimulus intensity and period were analyzed using a one-dimensional mapping called the phase transition curve (PTC) extended by Maginu. The PTC clarified how(More)
In the Hodgkin-Huxley equations (HH), we have identified the parameter regions in which either two stable periodic solutions with different amplitudes and periods and an equilibrium point or two stable periodic solutions coexist. The global structure of bifurcations in the multiple-parameter space in the HH suggested that the bistabilities of the periodic(More)
A neuron can respond to periodic inhibitory input with a variety of complex behaviors, periodic and aperiodic. We present a succession of models to test hypotheses for mechanisms underlying complex behavior generation. Model comparison using non-linear dynamics techniques indicates that long-duration IPSP aftereffects and spiking behavior are necessary for(More)