Computational Electrophysiology Dynamical Systems and Bifurcations
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 ha
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hinji Doi • Junko Inoue Kunichika Tsumoto
•
Zhenxing Pan
Computational Electrophysiology Dynamical Systems and Bifurcations
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Shinji Doi Professor Graduate School of Engineering Kyoto University Kyoto-Daigaku Katsura, Nishikyo-ku Kyoto 615-8510, Japan [email protected]
Zhenxing Pan Doctoral candidate Graduate School of Engineering Osaka University 2-1 Yamadaoka, Suita Osaka 565-0871, Japan [email protected]
Junko Inoue Associate Professor Faculty of Human Science Kyoto Koka Women’s University 38 Kadono-cho, Nishikyogoku, Ukyo-ku Kyoto 615-0882, Japan [email protected]
Kunichika Tsumoto Specially Appointed Assistant Professor The Center for Advanced Medical Engineering and Informatics Osaka University 2-2 Yamadaoka, Suita Osaka 565-0871, Japan [email protected]
ISBN 978-4-431-53861-5 e-ISBN 978-4-431-53862-2 DOI 10.1007/978-4-431-53862-2 Springer Tokyo Dordrecht Heidelberg London New York Library of Congress Control Number: 2009943556 R MATLAB is a registered trademark of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 017602098, USA. http://www.mathworks.com
c Springer 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. c MEIcenter Cover Illustration: Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Life is a dynamic, ambiguous, and fleeting system. Computational biology and systems biology use mathematical or computational models, usually denoted as dynamical systems such as difference equations or differential equations, for the analysis and understanding of such biological systems. In general, these models include many parameters, and these parameters inherently possess much ambiguity or uncertainty; thus it is important to treat the models with the consideration of such parameter uncertainty or changes. Bifurcation theory in nonlinear dynamical systems provides us with a powerful tool for the analysis of the effect of parameter change on a system and detects a critical parameter value when the qualitative nature of the system changes, whereas numerical or computer simulations give us only one solution under a fixed set of parameter values and initial values. Our aim is to provide an introduction to computational electrophysiology, particularly to the nonlinear dynamics of Hodgkin–Huxley (HH)-type models, together with a brief introduction to the dynamical system and to bifurcation analysis. This textbook includes many examples of numerical computations of bifurcation analysis on various models, r
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