Discrete Dynamical Systems / Edition 1

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Overview

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.

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Editorial Reviews

From the Publisher
From the reviews:

"Discrete dynamical systems are an interesting subject both for mathematicians and for applied scientists. This book is an introduction to this topic. It consists of 6 chapters. The first one focuses on the analysis of the evolution of state variables in one dimensional first-order autonomous linear systems. The second chapter develops the solutions for multidimensional first-order autonomous linear systems. … The presentation is clear and systematic. … it is for advanced undergraduate and graduate students in mathematics and applied scientists. e.g. economy, biology etc." (Ahmed Hegazi, Zentralblatt MATH, Vol. 1107 (9), 2007)

"The book under review gives an elementary introduction to the theory of discrete dynamical systems. … The presentation is clear and systematic. … ‘the book is designed for advanced undergraduate and graduate students in the fields of demography, ecology, economics, engineering, evolutionary biology, finance, mathematics, and physics’ with some basic knowledge in linear algebra and differential calculus." (Christian Pötzsche, Mathematical Reviews, Issue 2008 c)

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Product Details

  • ISBN-13: 9783642071850
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/6/2010
  • Edition description: 2007
  • Edition number: 1
  • Pages: 153
  • Product dimensions: 0.36 (w) x 9.21 (h) x 6.14 (d)

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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