Discrete Dynamical Systems and Difference Equations with Mathematica

Mustafa R.S. Kulenovic, Orlando Merino

344 pages, parution le 21/03/2002

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Résumé

Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and find basins of attraction. Modern computer algebra systems have opened the door to the use of symbolic calculation for studying difference equations. This book offers an introduction to discrete dynamical systems and difference equations and presents the Dynamica software. Developed by the authors and based on Mathematica, Dynamica provides an easy-to-use collection of algebraic, numerical, and graphical tools and techniques that allow users to quickly gain the ability to:· Find and classify the stability character of equilibrium and periodic points· Perform semicycle analysis of solutions· Calculate and visualize invariants · Calculate and visualize Lyapunov functions and numbersú Plot bifurcation diagramsú Visualize stable and unstable manifoldsú Calculate Box DimensionWhile presenting the essential theoretical concepts and results, the emphasis is on using the software. The authors present two sets of Dynamica sessions: one that serves as a tutorial of the different techniques, the other features case studies of well-known difference equations. Dynamica and notebooks corresponding to particular chapters are available for download from the Internet.

Contents

Dynamics of One-Dimensional Dynamical Systems
Dynamics of Two-Dimensional Dynamical Systems
Systems of Difference Equations, Stability, And Semicycles
Invariants and Related Lyapunov Functions
Dynamics of Three-Dimensional Dynamical Systems
Fractals Generated by Iterated Functions Systems

Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Mustafa R.S. Kulenovic, Orlando Merino
Parution	21/03/2002
Nb. de pages	344
Format	16 x 24
Couverture	Relié
Poids	671g
Intérieur	Noir et Blanc
EAN13	9781584882879
ISBN13	978-1-58488-287-9