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

Language: English

Published by Springer, J.B. Metzler Aug 2003, 2003

3540403272 / 9783540403272

Series: Book 69 of 126 - Lecture Notes in Economics and Mathematical Systems

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 204 pp. Englisch. …

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Title
Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games
Author
Werner Krabs
Publisher
Springer, J.B. Metzler Aug 2003
Publication year
2003
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3540403272
ISBN 13
9783540403272
Item weight
318 grams
Dimensions
235x155x12 mm
Series
Book 69 of 126: Lecture Notes in Economics and Mathematical Systems

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