Discrete Dynamical Systems

by Oded Galor

This book provides an introduction to discrete dynamical systems -- a framework of analysis commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. The book characterizes the fundamental factors that govern the qualitative and quantitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors the govern the evolution of state variables in the elementary context of one-dimensional, first-order, linear, autonomous systems. The fundamental insights about the forces that affect the evolution of these elementary systems are subsequently generalized, and the determinants of the trajectory of multi-dimensional, nonlinear, higher-order, non-autonomous dynamical systems are established.

MoreLess

Year of publication:	2007
Authors:	Galor, Oded
Publisher:	Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg
Subject:	Dynamisches System \| Diskretes System \| Frühe Neuzeit (16./17. Jahrhundert)
Description of contents:	Table of Contents [swbplus.bsz-bw.de] ; Description [swbplus.bsz-bw.de] ; Description [zbmath.org]

Online Resource

Check full text access |

More access options

Check Google Scholar

In libraries world-wide (WorldCat)

In German libraries (KVK)

subito order

I need help

Extent:	Online-Ressource (XIV, 153p. 53 illus, digital)
Series:	SpringerLink / Bücher
Type of publication:	Book / Working Paper
Language:	English
Notes:	Includes bibliographical references (p. [149]) and index Acknowledgements; Preface; Contents; 1 One-Dimensional, First-Order Systems; 1.1 Linear Systems; 1.1.1 Characterization of the Solution; 1.1.2 Existence of Steady-State Equilibria; 1.1.3 Uniqueness of Steady-State Equilibria; 1.1.4 Stability of Steady-State Equilibria; 1.2 Nonlinear Systems; 1.2.1 The Solution; 1.2.2 Existence, Uniqueness and Multiplicity of Steady-State Equilibria; 1.2.3 Linearization and Local Stability of Steady-State Equilibria; 1.2.4 Global Stability; 2 Multi-Dimensional, First-Order, Linear Systems: Solution; 2.1 Characterization of the Solution 2.2 Existence and Uniqueness of Steady-State Equilibria2.3 Examples of Two-Dimensional Systems; 2.3.1 Explicit Solution and Stability Analysis; 2.3.2 Stability Analysis Without an Explicit Solution; 2.4 Properties of the Jordan Matrix; 2.5 Representation of the System in the Jordan Normal Form; 2.5.1 Transformation of Non-Homogeneous Systems into Homogeneous Ones; 2.5.2 The Solution in Terms of the Jordan Normal Form; 3 Multi-Dimensional, First-Order, Linear Systems: Characterization; 3.1 Distinct Real Eigenvalues; 3.1.1 Characterization of the Solution 3.1.2 Phase Diagrams of Two-Dimensional Uncoupled Systems3.2 Repeated Real Eigenvalues; 3.2.1 Characterization of the Solution; 3.2.2 Phase Diagram of the Two-Dimensional Case; 3.3 Distinct Pairs of Complex Eigenvalues; 3.3.1 Characterization of the Solution; 3.3.2 Phase Diagram of a Two-Dimensional System; 3.4 Repeated Pairs of Complex Eigenvalues; 3.5 The General Case; 3.6 Characterization of Two-Dimensional Systems in Terms of tr A and det A; 4 Multi-Dimensional, First-Order, Nonlinear Systems; 4.1 Local Analysis; 4.1.1 Linearization; 4.1.2 Stable, Unstable, and Center Eigenspaces 4.1.3 Local Stable and Unstable Manifolds4.1.4 The Stable Manifold Theorem; 4.2 Global Analysis; 5 Higher-Order and Non-Autonomous Systems; 5.1 Higher-Order Systems; 5.1.1 Linear Systems; 5.1.2 Nonlinear Systems; 5.2 Non-Autonomous Systems; 6 Examples of Two-Dimensional Systems; 6.1 First-Order Linear Systems; 6.1.1 Real, Distinct, Positive Eigenvalues; 6.1.2 Complex Eigenvalues Periodic Orbit; 6.1.3 Complex Eigenvalues Spiral Sink; 6.2 Second-Order Linear Systems; 6.3 Nonlinear Systems; Glossary; References; Index
ISBN:	978-3-540-36776-5 ; 978-3-540-36775-8
Other identifiers:	10.1007/3-540-36776-4 [DOI]
Classification:	Gewöhnliche Differentialgleichungen ; Nichtlineare Dynamik ; Methoden und Techniken der Volkswirtschaft
Source:	ECONIS - Online Catalogue of the ZBW

Persistent link: https://www.econbiz.de/10013522893