Abstract:
: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 relation of the neuronal model is monotonic rather than the N-shaped one of the A-current. In this paper, we extend the previous results and show that the very slow spiking generically appears in both the three-dimensional Hodgkin-Huxley equations and the three dimensional Bonhoeffer-van der Pol (or FitzHugh-Nagumo) equations. The generation of repetitive discharges or the destabilization of the unique equilibrium point (resting potential) is a simple Hopf bifurcation. We also show that the generation of slow spiking does not depend on the stability of the Hopf bifurcation: supercritical or subcritical. The dynamics of slow spiking is investigated in detail and we demonstrate that the phenomenology of slow spiking can be categorized into two types according to the type of the corresponding bifurcation of a fast subsystem: Hopf or saddle-node bifurcation.
journal_name
J Comput Neuroscijournal_title
Journal of computational neuroscienceauthors
Doi S,Kumagai Sdoi
10.1007/s10827-005-2895-1subject
Has Abstractpub_date
2005-12-01 00:00:00pages
325-56issue
3eissn
0929-5313issn
1573-6873journal_volume
19pub_type
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