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* BIFURCATION DIAGRAM OF LOGISTIC EQUATION MODEL *
WHAT IS IT?
This model is an application of the famous Bifurcation diagram of logistic equation X[t+1] = k * X[t] * (1 - X[t]); with k=0..4 and X[t]=0..1
HOW IT WORKS
There are up to 10,000 turtles that has the job of paint one single point at X[t+1] on each iteration (In fact, only 400 turtles can be drawn, because the canvas is 400x200 pixels). The graphic represents each application of logistic equation over some value of the parameter k, remember that k is in [0,4] interval.
The first 40 iterates don't drawn any point, but you can see how is the dinamic behaviour.
HOW TO USE IT
SETUP button: Initialize the model, draw axes, optionally draw grid with 10 segments, and set up all turtles (SAMPLES in the model).
Go: kx(1-x) and GO buttons: run the model
SAMPLES slider: create <samples> number of turtles (values of k)
x0 slider: setup the X value. This variable don't have effect, because initial conditions are not drawn.
kMin: setup the lowest limit of k
kMax: setup the greatest limit of k
rnd-color?: Boolean variable that its useful if you want to draw each point with a different color, to see (in long term) a vertical line of the same color.
grid?: Boolean variable that establish the grid with 10 horizontal and vertical divisions
The model works with 2 initial parameters: k and X.
Press SETUP, then Go [ or GO (1-step) for 1 iteration ]
THINGS TO NOTICE
- Set 20 samples to apreciate all points of graphic into each application
THINGS TO TRY
- set 400 samples and 200 iterations (time = 200)
EXTENDING THE MODEL
You can write code for change vertical scale.
The Lorenz system; Rabbits Grass Weeds model; Wolves and sheep; Logistic Growth.
CREDITS AND REFERENCES
To refer to this model in academic publications, please use:
Caceres-Gonzalez, Abdiel E. "Bifurcation Diagram of Logistic Equation Model". Universidad Ju‡rez Aut—noma de Tabasco, DACB. Complex Systems and Theoretical Computer Foundations Group. Cunduac‡n, Tabasco, MŽxico. June 2007. http://computacion.cs.cinvestav.mx/~acaceres/resources/software/NetLogoModels/LogisticEq/bifurcacion2.nlogo
CONTACT THE AUTHOR
Abdiel E. Caceres-Gonzalez,
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