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Difference Equations and Chaos in Mathematica

Rob Knapp
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Mark Sofroniou
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Journal / Anthology

Dr. Dobb's Journal
Year: 1997
Issue: November
Page range: 84-90

A difference equation (or map) of the form x_n-1 = f(x_n, x_n-1, ...) which, together with some specified values or initial conditions defines a sequence {x_n}. Despite the seemingly simple form, difference equations have a variety of applications and can display a range of dynamics. Since maps describe iterative processes, they come up frequently in computer science. Also, many of the approximations in numerical analysis (such as numerical solutions of differential equations) typically approximate continuous dynamical systems using discrete systems of difference equations. Modeling a map using a computer is equivalent to studying the process of functional composition or functional iteration.

*Mathematics > Calculus and Analysis > Dynamical Systems
*Wolfram Technology > Programming > Equation Solving