7 edition of Discrete dynamical systems and difference equations with Mathematica found in the catalog.
Includes bibliographical references (p. 327-339) and index.
|Statement||Mustafa R.S. Kulenović, Orlando Merino.|
|LC Classifications||QA431 .K838 2002|
|The Physical Object|
|Pagination||xv, 344 p. :|
|Number of Pages||344|
|LC Control Number||2002017485|
We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to by: 3. Chapter 6 Modeling with Discrete Dynamical Systems LINEAR FIRST ORDER DIFFERENCE EQUATIONS Analytical Solutions Possibly the simplest nontrivial diﬀerence equation has the form xn+1 = axn. () This equation has the special solution xn = 0. Since it is constant it is said to be an equilibrium Size: KB.
Differential equations, dynamical systems, and an introduction to chaos/Morris W. Hirsch, Stephen Smale, Robert L. Devaney. p. cm. Rev. ed. of: Differential equations, dynamical systems, and linear algebra/Morris W. Hirsch and Stephen Smale. Includes bibliographical references and index. ISBN (alk. paper). Mathematical models of population dynamics have created great interest in the field of difference equations. As pointed out in [1, 2], to model biological phenomenon, discrete dynamical systems are more appropriate than continuous time models, being computationally efficient to get numerical results. Difference equations also appear naturally Cited by: 7.
Discrete-Time Dynamical Systems This video shows how discrete-time dynamical systems may be induced from continuous-time systems. Digital control 8: Stability of discrete-time systems This video is part of the module Control Systems at Stellenbosch University, South. Dear Colleagues, A dynamic system is characterized by three major components: phase space, evolution operator(s), and time scale. Discrete dynamic systems are governed by difference equations which may result from discretizing continuous dynamic systems or modeling evolution systems for which the time scale is discrete.
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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:Cited by: Discrete Dynamical Systems and Difference Equations with Mathematica -- from Wolfram Library Archive This books combines an introductory survey of theory and techniques of discrete dynamical systems and difference equations with a manual for the use of the software package Dynamica.
Discrete Dynamical Systems and Difference Equations with Mathematica. Discrete Dynamical Systems and Difference Equations with Mathematica book. By Mustafa R.S.
Kulenovic, Orlando Merino. Edition 1st Edition. First Published eBook Published 27 February Author: Mustafa R.S. Kulenovic, Orlando Merino. This books combines an introductory survey of theory and techniques of discrete dynamical systems and difference equations with a manual for the use of the software package Dynamica.
Many applications are presented as exercises and research projects. Following the work of Yorke and Li inthe 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 baCited by: The conference brought together leading researchers working in the respective fields to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations.
This book appeals to researchers and scientists working in the fields of difference equations and discrete dynamical systems and.
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. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences.
Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in. Differential equation describes the continuous time evaluation of the system, whereas discrete-time equation describes the discrete time evaluation of the system.
The theory of discrete dynamical. ISBN: OCLC Number: Description: xv, pages: illustrations ; 24 cm: Contents: 1. Dynamics of One-Dimensional Dynamical Systems --Linear Difference Equations with Constant Coefficients --Linear Difference Equations with Variable Coefficients --Stability --Stability in the Nonhyperbolic Case --Bifurcations --Dynamica Session --Symbolic Dynamics for One.
Discrete dynamical systems and difference equations with Mathematica. [M R S Kulenović; Orlando Merino] -- An introductory survey on the theory and techniques of discrete dynamical systems and difference equations as well as a manual for the use of the software package called Dynamica, which is used for.
Topics will include Discrete Dynamical Systems, Difference Equations, Stability Analysis, Phase Portraits, Bifurcation, and Chaos. This is a course that will count as one of the required or above courses for a math major or minor.
Prerequisites: Calculus II, Linear Algebra. Difference Equations or Discrete Dynamical Systems is a diverse field which impacts almost every branch of pure and applied mathematics. Not surprisingly, the techniques that are developed vary just as broadly. No more so is this variety reflected than at the prestigious annual International Conference on Difference Equations and Applications.
This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July The conference brou Advances in Difference Equations and Discrete Dynamical Systems ICDEA, Osaka, Japan, July Editors Buy Physical Book Learn about.
Chapter Discrete dynamical systems § The logistic equation § Fixed and periodic points § Linear diﬀerence equations § Local behavior near ﬁxed points Chapter Discrete dynamical systems in one dimension § Period doubling § Sarkovskii’s theorem § On the.
Discrete Dynamical Systems and Difference Equations with Mathematica eBook: Kulenovic, Mustafa R.S., Merino, Orlando: : Kindle StoreAuthor: Mustafa R.S. Kulenovic, Orlando Merino. Following the work of Yorke and Li inthe 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. Wolfram Research, makers of Mathematica, the only fully integrated technical computing software.
Wolfram Books. SEARCH: Discrete Dynamical Systems and Difference Equations with Mathematica. Authors: Mustafa R. Kulenovic, Orlando Merino. ISBN: (Hardcover). Stephen Lynch Dynamical Systems with Applications Using MathematicaR provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package.
The book has a very hands-on approach and takes the reader from basic theory to recently published research material. This chapter provides an overview of the discrete dynamical systems. Dynamical systems are mathematical models of how things move. The motion of the bodies in the solar system comes to mind as a physical dynamical system.
The moons and planets move in fairly complicated ways around the sun and one another, each exerting forces on the others.
These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems.
The conference was organized by.This book covers topics like stability, hyperbolicity, bifurcation theory and chaos, which are essential in order to understand the fascinating behavior of nonlinear discrete dynamical systems. This is a free eBook for students.The book provides detailed coverage of dynamics and phase diagrams, including: quantitative and qualitative dynamic systems, continuous and discrete dynamics, linear and non-linear systems and single equation and systems of equations.
It illustrates dynamic systems using Mathematica, Maple V and : Ronald Shone.