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23.—Oscillation Phenomena in the Hodgkin-Huxley Equations

Published online by Cambridge University Press:  14 February 2012

William C. Troy  and
J. B. McLeod
William C. Troy
Affiliation:
Department of Mathematics, University of Pittsburgh.
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Synopsis

A widely accepted model of nerve conduction in the squid axon is the systemof four non-linear partial differential equations developed by Hodgkin and Huxley. Under space clamp and current clamp conditions these equations are reduced to a system of ordinary differential equations.

We find that under appropriate assumptions on the functions and parameters in the resulting fourth order Hodgkin-Huxley equations there occurs a bifurcation of periodic solutions from the steady state. This bifurcation takes place as the current parameter, I, passes through a critical value.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 299 - 310
Copyright
Copyright © Royal Society of Edinburgh 1976

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