Book Review: Nonlinear dynamics in physiology and medicine

Abstract

This book deals with the application of mathematics in modeling and understanding physiological systems, especially those involving rhythms. It is divided roughly into two sections. In the first part of the book, the authors introduce ideas and techniques from nonlinear dynamics that are relevant to the analysis of biological rhythms. The second part consists of five in-depth case studies in which the authors use the theoretical tools developed earlier to investigate a number of physiological processes: the dynamic of excitable nerve and cardiac tissue, resetting and entrainment of biological oscillators, the effects of noise and time delay on the pupil light reflex, pathologies associated with blood cell replication, and Parkinsonian tremor. This book will be of interest to students and researchers in the natural and physical sciences wanting to learn about the complexities and subtleties of physiological systems from a mathematical perspective. 1. Theoretical Approaches in Physiology / Michael C. Mackey and Anne Beuter -- 2. Introduction to Dynamics in Nonlinear Difference and Differential Equations / Jacques Belair and Leon Glass -- 3. Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems / Michael R. Guevara -- 4. Dynamics of Excitable Cells / Michael R. Guevara -- 5. Resetting and Entraining Biological Rhythms / Leon Glass -- 6. Effects of Noise on Nonlinear Dynamics / Andre Longtin -- 7. Reentry in Excitable Media / Marc Courtemanche and Alain Vinet -- 8. Cell Replication and Control / Michael C. Mackey, Caroline Haurie and Jacques Belair -- 9. Pupil Light Reflex: Delays and Oscillations / John Milton -- 10. Data Analysis and Mathematical Modeling of Human Tremor / Anne Beuter, Roderick Edwards and Michele S. Titcombe -- A. An Introduction to XPP / Michael C. Mackey -- B. An Introduction to Matlab / Michele S. Titcombe and Caroline Haurie -- C. Time Series Analysis / Roderick Edwards and Michele S. Titcombe.