Dynamical Systems in Population Biology

✍ Scribed by Xiao-Qiang Zhao (auth.)

• Publisher: Springer-Verlag New York
• Year: 2003
• Tongue: English
• Leaves: 285
• Series: Canadian Mathematical Society / Société mathématique du Canada
• Edition: 1
• Category: Library

✦ Synopsis

The conjoining of nonlinear dynamics and biology has brought about significant advances in both areas, with nonlinear dynamics providing a tool for understanding biological phenomena and biology stimulating developments in the theory of dynamical systems. This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, traveling waves, and global analysis of typical models in population biology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems.

Dr. Xiao-Qiang Zhao is a professor in applied mathematics at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 40 papers and his research has played an important role in the development of the theory of periodic and almost periodic semiflows and their applications.

✦ Table of Contents

Front Matter....Pages i-xiii
Dissipative Dynamical Systems....Pages 1-35
Monotone Dynamics....Pages 37-61
Nonautonomous Semiflows....Pages 63-99
A Discrete-Time Chemostat Model....Pages 101-110
N -Species Competition in a Periodic Chemostat....Pages 111-132
Almost Periodic Competitive Systems....Pages 133-158
Competitor—Competitor—Mutualist Systems....Pages 159-188
A Periodically Pulsed Bioreactor Model....Pages 189-216
A Nonlocal and Delayed Predator—Prey Model....Pages 217-239
Traveling Waves in Bistable Nonlinearities....Pages 241-260
Back Matter....Pages 261-276

✦ Subjects

Dynamical Systems and Ergodic Theory; Genetics and Population Dynamics