Authors:
- First volume in a new series that covers emerging topics in the field of Applied Dynamical Systems
- Intended for mathematicians and biologists, as well as advanced graduate students
- Uses practical tutorials to example important connections between mathematics and physiology
- Includes supplementary material: sn.pub/extras
Part of the book series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials (FIADS, volume 1)
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Table of contents (2 chapters)
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Front Matter
About this book
This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently.
The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes.
Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells
Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium
Authors and Affiliations
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Department of Mathematics, Florida State University, Tallahasse, USA
Richard Bertram
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Department of Mathematics and Biological, Florida State University, Tallahassee, USA
Joel Tabak
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Department of Mathematical Sciences, Indiana University-Purdue University Ind, Indianapolis, USA
Wondimu Teka
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Department of Mathematics and Statistics, Boston University, Boston, USA
Theodore Vo
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Department of Mathematics, University of Sydney, Sydney, Australia
Martin Wechselberger
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Deparment of Mathematics, The University of Auckland, Private Bag, New Zealand
Vivien Kirk
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Department of Mathematics, University of Auckland, Auckland, New Zealand
James Sneyd
About the authors
Professor Richard Bertram is a Mathematics Professor at Florida State University. His current academic interests include the intersection between biology and mathematics.
Professor James Sneyd is a Professor in Applied Mathematics at The University of Auckland and his current research interests include mathematical physiology and nonlinear dynamical systems.
Bibliographic Information
Book Title: Mathematical Analysis of Complex Cellular Activity
Authors: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger, Vivien Kirk, James Sneyd
Series Title: Frontiers in Applied Dynamical Systems: Reviews and Tutorials
DOI: https://doi.org/10.1007/978-3-319-18114-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2015
Softcover ISBN: 978-3-319-18113-4Published: 23 October 2015
eBook ISBN: 978-3-319-18114-1Published: 09 October 2015
Series ISSN: 2364-4532
Series E-ISSN: 2364-4931
Edition Number: 1
Number of Pages: XII, 107
Number of Illustrations: 12 b/w illustrations, 25 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Applications of Nonlinear Dynamics and Chaos Theory, Physiological, Cellular and Medical Topics