An introduction to the mathematical, computational, and analytical
techniques used for modeling biological rhythms, presenting tools from
many disciplines and example applications.
All areas of biology and medicine contain rhythms, and these behaviors
are best understood through mathematical tools and techniques. This book
offers a survey of mathematical, computational, and analytical
techniques used for modeling biological rhythms, gathering these methods
for the first time in one volume. Drawing on material from such
disciplines as mathematical biology, nonlinear dynamics, physics,
statistics, and engineering, it presents practical advice and techniques
for studying biological rhythms, with a common language.
The chapters proceed with increasing mathematical abstraction. Part I,
on models, highlights the implicit assumptions and common pitfalls of
modeling, and is accessible to readers with basic knowledge of
differential equations and linear algebra. Part II, on behaviors,
focuses on simpler models, describing common properties of biological
rhythms that range from the firing properties of squid giant axon to
human circadian rhythms. Part III, on mathematical techniques, guides
readers who have specific models or goals in mind. Sections on
"frontiers" present the latest research; "theory" sections present
interesting mathematical results using more accessible approaches than
can be found elsewhere. Each chapter offers exercises. Commented MATLAB
code is provided to help readers get practical experience.
The book, by an expert in the field, can be used as a textbook for
undergraduate courses in mathematical biology or graduate courses in
modeling biological rhythms and as a reference for researchers.
