Discrete "Dynamical" Systems and Difference Equations with Mathematica

ISBN-10: 1584882875
ISBN-13: 9781584882879
Edition: 2002
List price: $154.95 Buy it from $146.55
eBook available
This item qualifies for FREE shipping

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

30 day, 100% satisfaction guarantee

If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost.

Learn more about our returns policy

Description: 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  More...

New Starting from $146.55
eBooks Starting from $61.98
Rent
Buy
what's this?
Rush Rewards U
Members Receive:
coins
coins
You have reached 400 XP and carrot coins. That is the daily max!
You could win $10,000

Get an entry for every item you buy, rent, or sell.

Study Briefs

Limited time offer: Get the first one free! (?)

All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.

Add to cart
Study Briefs
Calculus 1 Online content $4.95 $1.99
Add to cart
Study Briefs
Algebra Online content $4.95 $1.99
Add to cart
Study Briefs
Introduction to Logic Online content $4.95 $1.99
Add to cart
Study Briefs
Business Math Formulas Online content $4.95 $1.99

Customers also bought

Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading

Book details

List price: $154.95
Copyright year: 2002
Publisher: CRC Press LLC
Publication date: 2/27/2002
Binding: Hardcover
Pages: 360
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 1.430
Language: English

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 numbers Plot bifurcation diagrams Visualize stable and unstable manifolds Calculate Box DimensionWhile it presents the essential theoretical concepts and results, the book's 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.

Dynamics of One-Dimensional Dynamical Systems
Introduction
Linear Difference Equations with Constant Coefficients
Linear Difference Equations with Variable Coefficients
Stability
Visualization of Orbits and Time Series
Stability in the Nonhyperbolic Case
The Case f'(x) = 1
The Case f'(x) = -1
Bifurcations
Sharkovsky's Theorem and Period Doubling
Dynamica Session
Orbits and Periodic Points
Stability and Multipliers
Bifurcation Diagrams
Lyapunov Numbers
Box Dimension
Symbolic Dynamics for One-Dimensional Maps
The Cantor Set
Symbolic Dynamics and Chaos in the Sense of Devaney
Dynamica Session
Dissipative Maps and Global Attractivity
Parametrization and the Poincare Functional Equation
Exercises
Dynamics of Two-Dimensional Dynamical Systems
Introduction
Linear Theory
Two-Dimensional Linear Systems
Powers of a Matrix and Jordan Normal Form
Second Order Linear Equations
Equilibrium Solutions
Examples
The Riccati Equation
The Riccati Number and Changes of Variables
The Case when A + [beta] = 0
The Case when A + [beta] [not equal] 0 and R = 1/4
The Case when A + [beta] [not equal] 0 and R [ 1/4
The Case when A + [beta] [not equal] 0 and R ] 1/4
Linearized Stability Analysis
Dynamica Session
Period-Doubling Bifurcation
Lyapunov Numbers
Box Dimension
Semicycle Analysis
Stable and Unstable Manifolds
Dynamica Session on Henon's Equation
Invariants
Lyapunov Functions, Stability, and Invariants
Dynamica Session on Lyness' Map
Dissipative Maps and Systems
Dynamica Session on a Rational Difference Equation
Stability analysis of the equilibrium
Prime Period-Two Solutions
Numerical Explorations
Area-Preserving Maps and Systems
Biology Applications Projects
Applications in Economics
Exercises
Systems of Difference Equations, Stability, and Semicycles
Introduction
Linear Theory
Jordan Normal Form
Linear Nonhomogeneous System
Linear Difference Equations of k-th Order
Stability of Linear Systems
Norms of Vectors and Matrices
Basic Notions of Stability
The Routh-Hurwitz and Schur-Cohn Criteria
Nonlinear Systems and Stability
Linearized Stability
Lyapunov Functions and Stability
Limit Sets and Invariant Manifolds
Dissipative Maps
Stability of Difference Equations
Semicycle Analysis
Dynamica Session on Semicycles
Lyness' Equation
Todd's Equation
Gingerbreadman Equation
Rational Equation
Conclusion
Exercises
Invariants and Related Lyapunov Functions
Introduction
Invariants for Linear Equations and Systems
Invariants and Corresponding Lyapunov Functions for Nonlinear Systems
Applications
Invariants of a Special Class of Difference Equations
Applications
Dynamica Session on Invariants
Introduction
An Invariant for Lyness-Type Equation
Specifying a Basis for the Invariant, Part I
Specifying a Basis for the Invariant, Part II
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
Numerical Explorations
Dissipative Difference Equation of Third Order
Introduction
Dynamica Session on Local Asymptotic Stability of Period-Two Solutions
Introduction
A Quadratic Equation Satisfied by Period-Two Solutions
Main Results
Conditions for Linearized Local Stability
Formulas for A and B in Terms of p, q
Bounds for A and B
Completion of the Proof of Stability
Dynamica Session on Todd's Difference Equation
Summary of Results and Open Problems
Biology Applications Projects
Exercises
Fractals Generated by Iterated Function Systems
Introduction
Basic Definitions and Results
Iterated Function Systems
Basic Results on Iterated Function Systems
Calculation of Box Dimension for IFS
Dynamica Session
Exercises
Bibliography
Index

×
Free shipping on orders over $35*

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

Learn more about the TextbookRush Marketplace.

×