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  3. Mathematical Aspects of Hodgkin-Huxley Neural Theory
  • Cited by 109
Publisher:
Cambridge University Press
Online publication date:
November 2011
Print publication year:
1987
Online ISBN:
9780511983955
DOI:
https://doi.org/10.1017/CBO9780511983955
Subjects:
Mathematics, Mathematical Biology, Mathematical Modeling and Methods, Geometry and Topology
Series:
Cambridge Studies in Mathematical Biology (7)
Information

Book description

This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.

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