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Dynamical Systems in Population Biology

  • Book
  • © 2003

Overview

Authors:
  1. Xiao-Qiang Zhao

    1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Canada

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Part of the book series: CMS Books in Mathematics (CMSBM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Dissipative Dynamical Systems

    • Xiao-Qiang Zhao
    Pages 1-35

  3. Monotone Dynamics

    • Xiao-Qiang Zhao
    Pages 37-61

  4. Nonautonomous Semiflows

    • Xiao-Qiang Zhao
    Pages 63-99

  5. A Discrete-Time Chemostat Model

    • Xiao-Qiang Zhao
    Pages 101-110

  6. N-Species Competition in a Periodic Chemostat

    • Xiao-Qiang Zhao
    Pages 111-132

  7. Almost Periodic Competitive Systems

    • Xiao-Qiang Zhao
    Pages 133-158

  8. Competitor—Competitor—Mutualist Systems

    • Xiao-Qiang Zhao
    Pages 159-188

  9. A Periodically Pulsed Bioreactor Model

    • Xiao-Qiang Zhao
    Pages 189-216

  10. A Nonlocal and Delayed Predator—Prey Model

    • Xiao-Qiang Zhao
    Pages 217-239

  11. Traveling Waves in Bistable Nonlinearities

    • Xiao-Qiang Zhao
    Pages 241-260

  12. Back Matter

    Pages 261-276
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Keywords

About this book

Population dynamics is an important subject in mathematical biology. A cen­ tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.

Reviews

From the reviews:

"This is a highly technical research monograph which will be mainly of interest to those working in the field of mathematical population dynamics. … The book provides a comprehensive coverage of the latest theoretical developments, particularly in the purely mathematical sophistications of the field … ." (Tony Crilly, The Mathematical Gazette, March, 2005)

"This book provides an introduction to the theory of periodic semiflows on metric spaces and their applications to population dynamics. … This book will be most useful to mathematicians working on nonlinear dynamical models and their applications to biology." (R.Bürger, Monatshefte für Mathematik, Vol. 143 (4), 2004)

"The main purpose of the book, in the author’s words, ‘is to provide an introduction to the theory of periodic semiflows on metric spaces’ and to apply this theory to a collection of mathematical equations from population dynamics. … The book presents its mathematical theory in a coherent and readable fashion. It should prove to be a valuable resource for mathematicians who are interested in non-autonomous dynamical systems and in their applications to biologically inspired models." (J. M. Cushing, Mathematical Reviews, 2004 f)

Authors and Affiliations

  • Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Canada

    Xiao-Qiang Zhao

About the author

 

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.

Bibliographic Information

  • Book Title: Dynamical Systems in Population Biology

  • Authors: Xiao-Qiang Zhao

  • Series Title: CMS Books in Mathematics

  • DOI: https://doi.org/10.1007/978-0-387-21761-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2003

  • Hardcover ISBN: 978-0-387-00308-5Due: 20 May 2003

  • eBook ISBN: 978-0-387-21761-1Published: 05 June 2013

  • Series ISSN: 1613-5237

  • Series E-ISSN: 2197-4152

  • Edition Number: 1

  • Number of Pages: XIII, 276

  • Topics: Dynamical Systems and Ergodic Theory, Genetics and Population Dynamics

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