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Mathematical Aspects of Hodgkin-Huxley Neural Theory [Pehme köide]

  • Formaat: Paperback / softback, 276 pages, kõrgus x laius x paksus: 216x139x16 mm, kaal: 358 g, Worked examples or Exercises
  • Sari: Cambridge Studies in Mathematical Biology
  • Ilmumisaeg: 05-Jun-2008
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521063884
  • ISBN-13: 9780521063883
Teised raamatud teemal:
  • Formaat: Paperback / softback, 276 pages, kõrgus x laius x paksus: 216x139x16 mm, kaal: 358 g, Worked examples or Exercises
  • Sari: Cambridge Studies in Mathematical Biology
  • Ilmumisaeg: 05-Jun-2008
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521063884
  • ISBN-13: 9780521063883
Teised raamatud teemal:
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.

Muu info

This book is an introduction to the study of mathematical models of electrically active cells.
Introduction
1(5)
Nerve conduction: The work of Hodgkin and Huxley
6(61)
The physiological problem
6(6)
A brief summary of Hodgkin and Huxley's conclusions
12(4)
The work of Hodgkin and Huxley
16(37)
The experimental results
16(23)
Derivation of the differential equations
39(14)
What the Hodgkin-Huxley equations describe
53(1)
Mathematical status of the Hodgkin-Huxley equations
53(14)
History
53(4)
Some successful numerical analysis of the Hodgkin-Huxley equations
57(8)
Drawbacks of the Hodgkin-Huxley equations
65(2)
Nerve conduction: Other mathematical models
67(7)
Earlier models
67(1)
The FitzHugh-Nagumo model
68(1)
The Zeeman model
69(1)
Modifications of the Hodgkin-Huxley equations
70(3)
Modifications in the description of potassium and sodium conductances
70(1)
The FitzHugh-Adelman model
71(1)
The Hunter-McNaughton-Noble models
71(2)
The Lecar-Nossal stochastic model
73(1)
Models of other electrically excitable cells
74(27)
Introduction
74(1)
The myelinated nerve fiber
75(6)
Striated muscle fiber
81(4)
Cardiac fibers
85(16)
The cardiac Purkinje fiber
85(13)
The Beeler-Reuter model of ventricular myocardial fiber
98(3)
Mathematical theory
101(79)
Introduction
101(1)
Basic theory
101(29)
Existence theorems and extension theorems
101(4)
Autonomous systems
105(1)
Equilibrium points
106(8)
Stability and asymptotic stability of solutions
114(16)
Periodic solutions
130(8)
Autonomous systems
130(4)
Periodic solutions of equations with a periodic forcing term
134(4)
Singularly perturbed equations
138(40)
Introduction
138(1)
Some examples
139(4)
Some theory of singularly perturbed systems
143(35)
Partial differential equations
178(2)
Mathematical analysis of physiological models
180(69)
Introduction
180(4)
Models derived from voltage-clamp experiments
184(65)
Nerve conduction models
184(32)
Analysis of the Noble model of the cardiac Purkinje fiber
216(33)
Appendix 249(4)
References 253