
Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games
Werner Krabs(Author)
Springer (Publisher)
Published on 26. August 2003
Book
Paperback/Softback
XII, 192 pages
978-3-540-40327-2 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 2003
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XII, 192 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 12 mm
Weight
318 gr
ISBN-13
978-3-540-40327-2 (9783540403272)
DOI
10.1007/978-3-642-18973-9
Schweitzer Classification
Person
Stefan Pickl ist seit 1980 Professor für Operations Research an der Universität der Bundeswehr München. Werner Krabs war Professor am Fachbereich Mathematik an der TU Darmstadt. Er wurde 1999 emeritiert.
Content
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.