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Difference Equations and Chaos in Mathematica
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| Organization: | Wolfram Research, Inc. |
| Department: | Kernel Technology |
| Organization: | Wolfram Research, Inc. |
| Department: | Kernel Technology |
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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.
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