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Discrete Dynamical Systems and Difference Equations with Mathematica
     

Discrete Dynamical Systems and Difference Equations with Mathematica

3.5 2
by Mustafa R.S. Kulenovic, Orlando Merino
 

ISBN-10: 1584882875

ISBN-13: 9781584882879

Pub. Date: 02/27/2002

Publisher: Taylor & Francis

This is both an introductory survey on the theory and techniques of di screte dynamical systems and difference equations and a users' manual for the software package Dynamica, developed by the authors. The Dynam ica package is based on the Mathematica software and is designed as a collection of tools for studying discrete dynamical systems and differ ence equations

Overview

This is both an introductory survey on the theory and techniques of di screte dynamical systems and difference equations and a users' manual for the software package Dynamica, developed by the authors. The Dynam ica package is based on the Mathematica software and is designed as a collection of tools for studying discrete dynamical systems and differ ence equations. It is simple to use, requiring no programming experien ce, and gives users a series of algebraic, numerical, and graphical te chniques they can quickly learn to employ to study complex difference equations. The book includes exercises and research project based on a pplications encountered in biology and economics.

Product Details

ISBN-13:
9781584882879
Publisher:
Taylor & Francis
Publication date:
02/27/2002
Edition description:
New Edition
Pages:
360
Product dimensions:
6.40(w) x 9.50(h) x 0.98(d)

Table of Contents

DYNAMICS OF ONE-DIMENSIONAL DYNAMICAL SYSTEMS
Introduction
Linear Difference Equations with Constant Coefficients
Linear Difference Equations with Variable Coefficients
Stability
Stability in the Non-Hyperbolic Case
Bifurcations
Dynamica Session
Symbolic Dynamics for One-Dimensional Maps
Dissipative Maps and Global Attractivity
Parametrisation and Poincaré Functional Equation
Exercises
DYNAMICS OF TWO-DIMENSIONAL DYNAMICAL SYSTEMS
Introduction
Linear Theory
Equilibrium Solutions
The Riccati Equation
Linearized Stability Analysis
Dynamica Session
Period Doubling Bifurcation
Lyapunov Numbers
Box Dimension
Semicycle Analysis
Stable and Unstable Manifold
Dynamica Session on Henon's Equation
Invariants
Lyapunov Functions, Stability, and Invariants
Dynamica Session on Lyness' Map
Dissipative Maps and Systems
Dynamica Session on Rational Difference Equations
Area-preserving Maps and Systems
Biology Applications Projects
Applications in Economics
Exercises
SYSTEMS OF DIFFERENCE EQUATIONS, STABILITY, AND SEMICYCLES
Introduction
Linear Theory
Stability of Linear Systems
The Routh-Hurwitz and Schur-Cohn Criterion
Nonlinear Systems and Stability
Limit Sets and Invariant Manifolds
Dissipative Maps
Stability of Difference Equations
Semicycle Analysis
Dynamica Session on Semicycles
Exercises
INVARIANTS AND RELATED LYAPUNOV FUNCTIONS
Introduction
Invariants for Linear Equations and Systems
Invariants and Corresponding Lyapunov Functions for Nonlinear Systems
Invariants of Special Class of Difference Equations
Applications
Dynamica Session on Invariants
Dynamica Session on Lyapunov Functions
Invariance under Lie Group Transformations
Exercises
DYNAMICS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS
Introduction
Dynamica Session on Third Order Difference Equations
Dissipative Difference Equation of Third Order
Dynamica Session on Local Asymptotic Stability of Period-Two Solution
Dynamica Session on Todd's Difference Equation
Biology Applications Projects
Exercises
FRACTALS GENERATED BY ITERATED FUNCTIONS SYSTEMS
Introduction
Basic Definitions and Results
Iterated Function System
Basic Results on Iterated Functions Systems
Calculation of Box Dimension for IFS
Dynamica Session
Exercises
BIBLIOGRAPHY
INDEX

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Discrete Dynamical Systems and Difference Equations with Mathematica 3.5 out of 5 based on 0 ratings. 2 reviews.
Anonymous More than 1 year ago
Guest More than 1 year ago
This book is expectional, the best I've ever read on this subject. If you're intereseted in this type of mathmatics you MUST read this book! You'll get nowhere without it...