Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games:
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 autonom...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
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| Ausgabe: | 1st ed. 2003 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
529 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (XII, 192 p) |
| ISBN: | 9783642189739 |
| DOI: | 10.1007/978-3-642-18973-9 |
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| 520 | |a 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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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-3-642-18973-9 |
| edition | 1st ed. 2003 |
| format | Electronic eBook |
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| index_date | 2024-07-03T15:15:35Z |
| indexdate | 2024-07-10T08:56:07Z |
| institution | BVB |
| isbn | 9783642189739 |
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| spelling | Krabs, Werner Verfasser aut Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games by Werner Krabs 1st ed. 2003 Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (XII, 192 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 529 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 Economics, general Mathematics, general Economic Theory/Quantitative Economics/Mathematical Methods Applications of Mathematics Game Theory, Economics, Social and Behav. Sciences Optimization Economics Management science Mathematics Economic theory Applied mathematics Engineering mathematics Game theory Mathematical optimization Stabilität (DE-588)4056693-6 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Zeitdiskretes System (DE-588)4127297-3 gnd rswk-swf Dynamisches Spiel (DE-588)4121154-6 gnd rswk-swf Steuerbarkeit (DE-588)4134713-4 gnd rswk-swf Dynamisches Spiel (DE-588)4121154-6 s Zeitdiskretes System (DE-588)4127297-3 s Stabilität (DE-588)4056693-6 s Steuerbarkeit (DE-588)4134713-4 s DE-604 Dynamisches System (DE-588)4013396-5 s Optimierung (DE-588)4043664-0 s Erscheint auch als Druck-Ausgabe 9783540403272 Erscheint auch als Druck-Ausgabe 9783642189746 https://doi.org/10.1007/978-3-642-18973-9 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Krabs, Werner Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games Economics, general Mathematics, general Economic Theory/Quantitative Economics/Mathematical Methods Applications of Mathematics Game Theory, Economics, Social and Behav. Sciences Optimization Economics Management science Mathematics Economic theory Applied mathematics Engineering mathematics Game theory Mathematical optimization Stabilität (DE-588)4056693-6 gnd Optimierung (DE-588)4043664-0 gnd Dynamisches System (DE-588)4013396-5 gnd Zeitdiskretes System (DE-588)4127297-3 gnd Dynamisches Spiel (DE-588)4121154-6 gnd Steuerbarkeit (DE-588)4134713-4 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4043664-0 (DE-588)4013396-5 (DE-588)4127297-3 (DE-588)4121154-6 (DE-588)4134713-4 |
| title | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games |
| title_auth | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games |
| title_exact_search | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games |
| title_exact_search_txtP | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games |
| title_full | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games by Werner Krabs |
| title_fullStr | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games by Werner Krabs |
| title_full_unstemmed | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games by Werner Krabs |
| title_short | Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games |
| title_sort | analysis controllability and optimization of time discrete systems and dynamical games |
| topic | Economics, general Mathematics, general Economic Theory/Quantitative Economics/Mathematical Methods Applications of Mathematics Game Theory, Economics, Social and Behav. Sciences Optimization Economics Management science Mathematics Economic theory Applied mathematics Engineering mathematics Game theory Mathematical optimization Stabilität (DE-588)4056693-6 gnd Optimierung (DE-588)4043664-0 gnd Dynamisches System (DE-588)4013396-5 gnd Zeitdiskretes System (DE-588)4127297-3 gnd Dynamisches Spiel (DE-588)4121154-6 gnd Steuerbarkeit (DE-588)4134713-4 gnd |
| topic_facet | Economics, general Mathematics, general Economic Theory/Quantitative Economics/Mathematical Methods Applications of Mathematics Game Theory, Economics, Social and Behav. Sciences Optimization Economics Management science Mathematics Economic theory Applied mathematics Engineering mathematics Game theory Mathematical optimization Stabilität Optimierung Dynamisches System Zeitdiskretes System Dynamisches Spiel Steuerbarkeit |
| url | https://doi.org/10.1007/978-3-642-18973-9 |
| work_keys_str_mv | AT krabswerner analysiscontrollabilityandoptimizationoftimediscretesystemsanddynamicalgames |