Discrete Dynamical Systems and Difference Equations with Mathematica

Book Description

Following a work of Yorke and Li in 1975, the idea of discrete dynamical systems and difference equations developed quickly. The applying difference equations also increased quickly, particularly with the development of graphical-interface software that may plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and discover basins of attraction.

Modern computer algebra systems have opened up the doorway to using symbolic calculation for studying difference equations. This book offers introducing discrete dynamical systems and difference equations and is definitely the Dynamica software. Produced by the authors and according to Mathematica, Dynamica offers an easy-to-use assortment of algebraic, statistical, and graphical techniques and tools that permit users to rapidly gain the opportunity to:
 

• Find and classify the soundness character of equilibrium and periodic points
• Perform semicycle analysis of solutions
• Calculate and visualize invariants
• Calculate and visualize Lyapunov functions and figures
• Plot bifurcation diagrams
• Visualize stable and unstable manifolds
• Calculate Box Dimension

  Although it is definitely the essential theoretical concepts and results, the book’s emphasis is on making use of the program. The authors present two teams of Dynamica sessions: one which works as a tutorial from the different techniques, another features situation studies of well-known difference equations. Dynamica and notebooks akin to particular chapters are for sale to download from the web.

Table of Contents

Dynamics for just one-Dimensional Difference Equations. Dynamics for 2-Dimensional Difference Equations. Systems of Difference Equations, Stability, and Semicycles. Invariants and Related Lyapunov Functions. Dynamics for 3-Dimensional Difference Equations. Fractals Generated by Iterated Functions Systems. Bibliography.