Werner Krabs

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

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Lecture Notes in Economics and Mathematical Systems 529
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-40327-2
• Softcover reprint of the original 1st ed. 2003
• Seitenzahl: 204
• Erscheinungstermin: 26. August 2003
• Englisch
• Abmessung: 235mm x 155mm x 12mm
• Gewicht: 328g
• ISBN-13: 9783540403272
• ISBN-10: 3540403272
• Artikelnr.: 12231161

Autorenporträt

Werner Krabs, Technical University of Darmstadt, Germany / Stefan Wolfgang Pickl, Universität zu Köln, Germany

Inhaltsangabe

Uncontrolled Systems.- Controlled Systems.- Controllability and Optimization.- A.1 The Core of a Cooperative n-Person Game.- A.2 The Core of a Linear Production Game.- A.3 Weak Pareto Optima: Necessary and Sufficient Conditions.- A.4 Duality.- B Bibliographical Remarks.- References.- About the Authors.