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Graphical Analysis for Discrete Dynamical Systems

Thomas LoFaro
Organization: Gustavus Adolphus College
Department: Department of Mathematics and Computer Science
URL: http://www.gac.edu/~tlofaro/
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GraphicalAnalysis.m is a Mathematica package designed to aid students and researchers in analyzing the dynamics of functions of a single real variable. The two main functions are PlotIterates and Bifurcation. Both of these functions provide a significant amount of flexibility and have been designed so that their syntax mimics that of most Mathematica commands. PlotIterates plots a function and generates stairstep diagrams. Multiple initial conditions can be specified and are color coded. The number of iterations and transients can be specified. The function ListIterates generates a list of iterates without the graphics. Bifurcation generates a bifurcation diagram of a family of function. Multiple initial conditions can be specified and can depend on the parameter. The number of iterations,transients and parameter values can be specified.

GAintro.nb provides an introduction to the capabilities of this package.

*Mathematica Technology > Programming > Graphing and Plotting
*Mathematics > Calculus and Analysis > Dynamical Systems

ListIterates, bifurcation, transient
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GAintro.nb (433.7 KB) - Mathematica notebook
GraphicalAnalysis.m (7.5 KB) - Mathematica package

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