Solutions to axon equations.

Abstract:

:The solutions to a general class of axon partial differential equations proposed by FitzHugh which includes the Hodgkin-Huxley equations are studied. It is shown that solutions to the partial differential equations are exactly the solutions to a related set of integral equations. An iterative procedure for constructing the solutions based on standard methods for ordinary differential equations is given and each set of initial values is shown to lead to a unique solution. Continuous dependence of the solutions on the initial values is established and solutions with initial values in a restricted (physiological) range are shown to remain in that range for all time. The iterative procedure is not suggested as the basis for numerical integration.

journal_name

Biophys J

journal_title

Biophysical journal

authors

Evans J,Shenk N

doi

10.1016/S0006-3495(70)86355-X

subject

Has Abstract

pub_date

1970-11-01 00:00:00

pages

1090-101

issue

11

eissn

0006-3495

issn

1542-0086

pii

S0006-3495(70)86355-X

journal_volume

10

pub_type

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