Skip to main content
SpringerLink
Log in
Book cover

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

  • Book
  • © 2003

Overview

Authors:
  1. Werner Krabs

    1. Department of Mathematics, Technical University Darmstadt, Darmstadt, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Stefan Wolfgang Pickl

    1. Department of Mathematics Center of Applied Computer Science, ZAIK University of Cologne, Cologne, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

Editors:
  1. M. Beckmann
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. H. P. Künzi
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  3. G. Fandel

    1. Fachbereich Wirtschaftswissenschaften, Fernuniversität Hagen, Hagen, Germany

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  4. W. Trockel

    1. Institut für Mathematische Wirtschaftsforschung (IMW), Universität Bielefeld, Bielefeld, Germany

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  5. C. D. Aliprantis
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  6. A. Basile
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  7. A. Drexl
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  8. G. Feichtinger
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  9. W. Güth
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  10. K. Inderfurth
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  11. P. Korhonen
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  12. W. Kürsten
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  13. U. Schittko
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  14. R. Selten
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  15. R. Steuer
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  16. F. Vega-Redondo
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 529)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (3 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Uncontrolled Systems

    • Werner Krabs, Stefan Wolfgang Pickl
    Pages 1-46

  3. Controlled Systems

    • Werner Krabs, Stefan Wolfgang Pickl
    Pages 47-92

  4. Controllability and Optimization

    • Werner Krabs, Stefan Wolfgang Pickl
    Pages 93-165

  5. Back Matter

    Pages 167-189
    Download chapter PDF
Back to top

Keywords

About this book

J. P. La Salle has developed in [20] a stability theory for systems of difference equations (see also [8]) which we introduce in the first chapter within the framework of metric spaces. The stability theory for such systems can also be found in [13] in a slightly modified form. We start with autonomous systems in the first section of chapter 1. After theoretical preparations we examine the localization of limit sets with the aid of Lyapunov Functions. Applying these Lyapunov Functions we can develop a stability theory for autonomous systems. If we linearize a non-linear system at a fixed point we are able to develop a stability theory for fixed points which makes use of the Frechet derivative at the fixed point. The next subsection deals with general linear systems for which we intro­ duce a new concept of stability and asymptotic stability that we adopt from [18]. Applications to various fields illustrate these results. We start with the classical predator-prey-model as being developed and investigated by Volterra which is based on a 2 x 2-system of first order differential equations for the densities of the prey and predator population, respectively. This model has also been investigated in [13] with respect to stability of its equilibrium via a Lyapunov function. Here we consider the discrete version of the model.

Authors, Editors and Affiliations

  • Fachbereich Wirtschaftswissenschaften, Fernuniversität Hagen, Hagen, Germany

    G. Fandel

  • Institut für Mathematische Wirtschaftsforschung (IMW), Universität Bielefeld, Bielefeld, Germany

    W. Trockel

  • Department of Mathematics, Technical University Darmstadt, Darmstadt, Germany

    Werner Krabs

  • Department of Mathematics Center of Applied Computer Science, ZAIK University of Cologne, Cologne, Germany

    Stefan Wolfgang Pickl

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation