Discrete Dynamical Systems / Edition 1

Discrete Dynamical Systems / Edition 1

by Oded Galor
     
 

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ISBN-10: 3540367756

ISBN-13: 9783540367758

Pub. Date: 12/12/2006

Publisher: Springer Berlin Heidelberg

This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical

Overview

This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative 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 those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.

Product Details

ISBN-13:
9783540367758
Publisher:
Springer Berlin Heidelberg
Publication date:
12/12/2006
Edition description:
2007
Pages:
153
Product dimensions:
6.10(w) x 9.25(h) x 0.02(d)

Related Subjects

Table of Contents

One-Dimensional, First-Order Systems.- Multi-Dimensional, First-Order, Linear Systems: Solution.- Multi-Dimensional, First-Order, Linear Systems: Characterization.- Multi-Dimensional, First-Order, Nonlinear Systems.- Higher-Order and Non-Autonomous Systems.- Examples of Two-Dimensional Systems.

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