Differenzengleichungen Und Diskrete Dynamische Systeme
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Differenzengleichungen Und Diskrete Dynamische Systeme
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Author : Ulrich Krause
language : de
Publisher: Springer-Verlag
Release Date : 2013-03-09
Differenzengleichungen Und Diskrete Dynamische Systeme written by Ulrich Krause and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Dieses Buch befaßt sich mit der mathematischen Analyse von dynamischen Prozes sen, deren zeitliche Entwicklung nicht kontinuierlich fließend, sondern in diskreten Zeit schritten modelliert wird. In den Naturwissenschaften, den Ingenieurwissenschaften und den Wirtschaftswissenschaften wird häufig bei der Untersuchung dynamischer Vorgänge zunächst ein Modell in diskreter Zeit formuliert, also eine Differenzengleichung oder ein (zeit-) diskretes dynamisches System. Anschließend wird dann gewöhnlich durch einen Grenzübergang, bei dem die Länge eines Zeitschritts gegen Null strebt, das diskrete Modell in eine oder mehrere Differentialgleichungen verwandelt. Dieses Vorgehen, das besonders in der Physik sehr erfolgreich ist mit Ausstrahlungen bis hin in die Sozialwis senschaften, hat den großen Vorteil, daß sich dabei das hochentwickelte mathematische Instrumentarium der Differentialgleichungen und differenzierbaren dynamischen Syste me anzapfen läßt. Ein Nachteil liegt jedoch darin, daß für eine numerische Auswertung des Modells zum Zwecke der empirischen Überprüfung, das kontinuierliche Modell wie der in ein diskretes Modell zurückverwandelt werden muß. Das scheint nicht nur ein Umweg zu sein, insbesondere angesichts eines zunehmenden Einsatzes von Computern, sondern birgt auch zusätzliche Probleme, da es trotz gewisser Analogien keine systemati schen Übersetzungsregeln zwischen Differentialgleichungen und Differenzengleichungen gibt, vor allem nicht, wenn nichtlineare Vorgänge im Spiel sind. Auch aus diesem Grund bildet sich mehr und mehr eine Tendenz heraus, das erstellte diskrete Modell direkt mit Methoden der Differenzengleichungen und diskreten dynamischen Systeme zu untersu chen; dieses Vorgehen ist etwa in der Biologie und derÖkonomie seit jeher gebräuchlicher als z. B. in der Physik.
Differenzengleichungen Und Diskrete Dynamische Systeme
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Author : Ulrich Krause
language : de
Publisher: Walter de Gruyter
Release Date : 2012-05-29
Differenzengleichungen Und Diskrete Dynamische Systeme written by Ulrich Krause and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-29 with Mathematics categories.
In seiner zweiten erweiterten und aktualisierten Auflage befasst sich dieses Lehrbuch mit der Theorie und den Anwendungen von dynamischen Prozessen, deren zeitliche Entwicklung nicht kontinuierlich, sondern in diskreten Zeitschritten durch Differenzengleichungen modelliert wird. Verstärkt noch durch den Einsatz von Computern spielen die diskreten Modelle eine zunehmend wichtige Rolle in den Natur-, Ingenieur- und Wirtschaftswissenschaften. Daher werden in dieser Neuauflage zusätzlich auch Anwendungen in der Finanzmathematik betrachtet. Nach einer grundlegenden Einführung mit Beispielen werden im ersten Teil lineare Systeme und ihre Stabilitätseigenschaften gründlich behandelt. Der zweite Teil befasst sich mit nichtlinearen Systemen, insbesondere deren Stabilität, und enthält einen Exkurs zu Chaos und Fraktalen sowie eine Einführung in die neuere Theorie positiver dynamischer Systeme nebst Anwendungen in Biologie und Ökonomie.
Neuere Entwicklungen In Der Theorie Dynamischer Systeme Und Ihre Bedeutung F R Die Agrar Konomie
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Author : Wolfgang Lentz
language : de
Publisher: Duncker & Humblot
Release Date : 2014
Neuere Entwicklungen In Der Theorie Dynamischer Systeme Und Ihre Bedeutung F R Die Agrar Konomie written by Wolfgang Lentz and has been published by Duncker & Humblot this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Business & Economics categories.
Dynamical Systems
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Author : Werner Krabs
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-03
Dynamical Systems written by Werner Krabs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-03 with Mathematics categories.
At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.
Analysis Controllability And Optimization Of Time Discrete Systems And Dynamical Games
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Author : Werner Krabs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Controllability And Optimization Of Time Discrete Systems And Dynamical Games written by Werner Krabs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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.
Geometric Theory Of Discrete Nonautonomous Dynamical Systems
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Author : Christian Pötzsche
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-17
Geometric Theory Of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-17 with Language Arts & Disciplines categories.
The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Dynamical Systems And Linear Algebra
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Author : Fritz Colonius
language : en
Publisher: American Mathematical Society
Release Date : 2014-10-03
Dynamical Systems And Linear Algebra written by Fritz Colonius and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-03 with Mathematics categories.
This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝd and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students.
Positive Dynamical Systems In Discrete Time
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Author : Ulrich Krause
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-03-10
Positive Dynamical Systems In Discrete Time written by Ulrich Krause and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-10 with Mathematics categories.
This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences. "The author has greatly expanded the field of positive systems in surprising ways." - Prof. Dr. David G. Luenberger, Stanford University(USA)
Progress On Difference Equations And Discrete Dynamical Systems
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Author : Steve Baigent
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Progress On Difference Equations And Discrete Dynamical Systems written by Steve Baigent and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.
This book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability. Other chapters cover the latest personal research contributions of the author(s) in their particular area of expertise and range from the more technical articles on abstract systems to those that discuss the application of difference equations to real-world problems. The book is of interest to both Ph.D. students and researchers alike who wish to keep abreast of the latest developments in difference equations and discrete dynamical systems.
Problems And Solutions Nonlinear Dynamics Chaos And Fractals
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Author : Willi-hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-03-02
Problems And Solutions Nonlinear Dynamics Chaos And Fractals written by Willi-hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Science categories.
This book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems.The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.