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written by Wolfgang Christian
The Logistic Map Fixed Points Model finds periodic trajectories of the logistic map such that n iterations of the map starting with an initial value x return to that value.  The key idea for this model is that for values of the logistic map control parameter r in the chaotic regime, there are periodic but unstable trajectories. This property of the chaotic regime means that if we choose the value of the seed x0 to be precisely equal to a point on an unstable trajectory with period n, the subsequent trajectory will have this period. However, if we choose a value of x0 that differs ever so slightly from this special value, the trajectory will not be periodic.  This model shows how to find these special values of x0.

The Logistic Map Fixed Points Model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_chaos_LogisticMapFixedPoints.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.6 of Java.
View the source code document attached to this resource
Subjects Levels Resource Types
General Physics
- Computational Physics
Mathematical Tools
- Numerical Analysis
Modern Physics
- Chaos & Non-linear Dynamics
Other Sciences
- Mathematics
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
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- Educators
- application/java
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Access Rights:
Free access
License:
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Wolfgang Christian
Record Cloner:
Metadata instance created January 29, 2012 by Wolfgang Christian
Record Updated:
July 15, 2013 by Matt Mohorn
Last Update
when Cataloged:
January 29, 2012
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Record Link
AIP Format
W. Christian, Computer Program LOGISTIC MAP FIXED POINTS MODEL, Version 1.0 (2012), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556).
AJP/PRST-PER
W. Christian, Computer Program LOGISTIC MAP FIXED POINTS MODEL, Version 1.0 (2012), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556>.
APA Format
Christian, W. (2012). Logistic Map Fixed Points Model (Version 1.0) [Computer software]. Retrieved April 16, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556
Chicago Format
Christian, Wolfgang. "Logistic Map Fixed Points Model." Version 1.0. http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556 (accessed 16 April 2014).
MLA Format
Christian, Wolfgang. Logistic Map Fixed Points Model. Vers. 1.0. Computer software. 2012. Java 1.6. 16 Apr. 2014 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556>.
BibTeX Export Format
@misc{ Author = "Wolfgang Christian", Title = {Logistic Map Fixed Points Model}, Month = {January}, Year = {2012} }
Refer Export Format

%A Wolfgang Christian
%T Logistic Map Fixed Points Model
%D January 29, 2012
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556
%O 1.0
%O application/java

EndNote Export Format

%0 Computer Program
%A Christian, Wolfgang
%D January 29, 2012
%T Logistic Map Fixed Points Model
%7 1.0
%8 January 29, 2012
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11682&DocID=2556


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Logistic Map Fixed Points Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Logistic Map Fixed Points Model.

relation by Wolfgang Christian

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