Computational electrophysiology: dynamical systems and bifurcations

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Biological systems inherently possess much ambiguity or uncertainty. Computational electrophysiology is the one area, from among the vast and rapidly growing discipline of computational and systems biology, in which computational or mathematical models have succeeded. This book provides a practical and quick guide to both computational electrophysiology and numerical bifurcation analysis. Bifurcation analysis is a very powerful tool for the analysis of such highly nonlinear biological systems. Bifurcation theory provides a way to analyze the effect of a parameter change on a system and to detect a critical parameter value when the qualitative nature of the system changes. Included in this work are many examples of numerical computations of bifurcation analysis of various models as well as mathematical models with different abstraction levels from neuroscience and electrophysiology. This volume will benefit graduate and undergraduate students as well as researchers in diverse fields of science.

Author(s): Shinji Doi, Junko Inoue, Zhenxing Pan, Kunichika Tsumoto (auth.)
Series: A First Course in “In Silico Medicine” 2
Edition: 1
Publisher: Springer Tokyo
Year: 2010

Language: English
Pages: 140
City: Tokyo; New York
Tags: Biomedical Engineering; Molecular Medicine; Medicinal Chemistry

Front Matter....Pages i-viii
A Very Short Trip on Dynamical Systems....Pages 1-35
The Hodgkin–Huxley Theory of Neuronal Excitation....Pages 37-54
Computational and Mathematical Models of Neurons....Pages 55-98
Whole System Analysis of Hodgkin–Huxley Systems....Pages 99-117
Hodgkin–Huxley-Type Models of Cardiac Muscle Cells....Pages 119-141
Back Matter....Pages 143-153