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© 2013

Nonautonomous Dynamical Systems in the Life Sciences

  • Peter E. Kloeden
  • Christian Pötzsche
  • Overview of recent developments in the theory of nonautonomous dynamical systems

  • Examples of concepts and techniques in the context of simple models from the life sciences

  • Representative collection of nonautonomous dynamical systems in the life sciences

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2102)

Also part of the Mathematical Biosciences Subseries book sub series (LNMBIOS, volume 2102)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Theoretical Basics

    1. Front Matter
      Pages 1-1
    2. Peter E. Kloeden, Christian Pötzsche
      Pages 3-39
    3. Michael Marcondes de Freitas, Eduardo D. Sontag
      Pages 41-87
    4. Martin Wechselberger, John Mitry, John Rinzel
      Pages 89-132
  3. Applications

    1. Front Matter
      Pages 133-133
    2. Philip T. Clemson, Spase Petkoski, Tomislav Stankovski, Aneta Stefanovska
      Pages 163-197
    3. Eva Herrmann, Yusuke Asai
      Pages 251-268
  4. Back Matter
    Pages 309-314

About this book

Introduction

Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.

Keywords

37B55,92XX,34C23,34C45,37HXX Models from the life sciences Nonautonomous bifurcations Nonautonomous dynamical systems

Editors and affiliations

  • Peter E. Kloeden
    • 1
  • Christian Pötzsche
    • 2
  1. 1.Institut für MathematikGoethe-Universität FrankfurtFrankfurt am MainGermany
  2. 2.Institut für MathematikAlpen-Adria Universität KlagenfurtKlagenfurt am WörtherseeAustria

Bibliographic information

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Reviews

“The book by Peter Kloeden and Christian Pötzsche meets an important need by addressing a topical and very general problem. … topics nicely illustrate the wide range of problems in the life sciences where nonautonomous dynamics can be important and, in many cases, is essential for an understanding of observed phenomena. The editors are to be commended for pulling together such a timely and interesting volume.” (Peter V. E. McClintock, Contemporary Physics, November, 2014)