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Nonautonomous Dynamical Systems in the Life Sciences

  • Book
  • © 2013

Overview

Editors:
  1. Peter E. Kloeden

    1. Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

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  2. Christian Pötzsche

    1. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt am Wörthersee, Austria

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    You can also search for this editor in PubMed   Google Scholar

  • 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

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

Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Theoretical Basics

    1. Front Matter

      Pages 1-1
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    2. Nonautonomous Dynamical Systems in the Life Sciences

      • Peter E. Kloeden, Christian Pötzsche
      Pages 3-39

    3. Random Dynamical Systems with Inputs

      • Michael Marcondes de Freitas, Eduardo D. Sontag
      Pages 41-87

    4. Canard Theory and Excitability

      • Martin Wechselberger, John Mitry, John Rinzel
      Pages 89-132

  3. Applications

    1. Front Matter

      Pages 133-133
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    2. Stimulus-Response Reliability of Biological Networks

      • Kevin K. Lin
      Pages 135-161

    3. Coupled Nonautonomous Oscillators

      • Philip T. Clemson, Spase Petkoski, Tomislav Stankovski, Aneta Stefanovska
      Pages 163-197

    4. Multisite Mechanisms for Ultrasensitivity in Signal Transduction

      • Germán A. Enciso
      Pages 199-224

    5. Mathematical Concepts in Pharmacokinetics and Pharmacodynamics with Application to Tumor Growth

      • Gilbert Koch, Johannes Schropp
      Pages 225-250

    6. Viral Kinetic Modeling of Chronic Hepatitis C and B Infection

      • Eva Herrmann, Yusuke Asai
      Pages 251-268

    7. Some Classes of Stochastic Differential Equations as an Alternative Modeling Approach to Biomedical Problems

      • Christina Surulescu, Nicolae Surulescu
      Pages 269-307

  4. Back Matter

    Pages 309-314
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Keywords

About this book

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.

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)

Editors and Affiliations

  • Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

    Peter E. Kloeden

  • Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt am Wörthersee, Austria

    Christian Pötzsche

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