VMI Chaos Lab, NetLogo Section
Notes
- These programs make use of NetLogo 2.1 models.
- Warning: it takes a couple of minutes to load an applet.
- With all our NetLogo models, click "setup" first.
Experiments for 1D iterations, Lab 1
- Graph of the logistic fuction with cobwebs
- This model draws trajectories of the logistic function
using the Koenig-Lemeray (KL) or cobweb method.
- Lab 1. Graph of the logistic function
(Load the applet into your browser) This is a model in NetLogo 4.1.3.
- How to run the model
- Set the family parameter, R, with the slider
- Click "setup"
- Click "step" several times to follow the trajectory
- Click "clear" and then "step" to reveal the attractor
- Suggestions
- Study the attractor for increasing values of R
-
Tutorial video for Lab #1, 7 minutes
Experiments for 1D iterations, Lab 2
- Response diagram of the logistic map family
- The response diagram is a graphical portrait
of the attractors of a scheme, that is, a family of maps.
In this case, the logistic family is used.
- Lab 2. Logistic Response
(Load the applet into your browser)
- How to run the model
- Click "setup"
- Click "make-it" to begin to draw the diagram
(button turns black)
- Wait for about 30 seconds or so to complete the proces
(button will turn blue again)
- Suggestions
- Begin with R-min = 0, and R-max = 4, for the full response diagram.
- Choose other combinations of R-min and R-max to stretch
out a thin vertical slice of the diagram.
- Try to find periodic windows within the chaotic regime.
-
Tutorial video for Lab #2, 6 minutes
Experiments for 2D iterations
- Iterations of the Dorband map family
- How to run the model
- Click "setup"
- Click "place-particles" (the button turns black)
- Move cursor into the Graphic Window (large black square)
and click to place a test particle (small green square)
- Repeat until you have a few well separated test particles
- Click "place-particles" again (the button turns blue again)
- Click "go" (the button turns black, the test particles
swiftly jump along their trajectories leaving red dots,
as each approaches its attractor)
- Click "go" again to stop the action (button turns blue again)
- Suggestions
- The parameter "c" is set by the slider, which may vary
from 0.0 to 1.0. Each setting of this slider determines one
map of the Dorband map family
- Find the attractors of the Dorband map
for various values of the parameter
- Hint: there is always either one or two attractors
- Fix a value of "c" using the slider
- Place some particles in initial positions
in the graphic window, which
shows the entire state space of the map, a
2D rectangle
- Press "go" and shortly after, press it again, to draw trajectories
for each of the particles
- Use the "clear" button the erase the trajectories drawn so far,
leaving the test particles (the small green squares reappear)
in their current positions
- Continue until you think you have found all the attractors
(red blotches)
Experiments for Basins of Attraction
- Iterations of a quartic map
- To be posted shortly
- This applet iterates a map with two basins.
The aim is to locate the basins by trial and error.
- Lab 4. Basins discovery
(Load the applet into your browser)
- How to run the model
- 1. setup clears and sets up everything
- 2. place-particles,
click the button,
then click Graphics Window to place only one particle,
click the button again to finish this step
- 3. click the go button to begin to draw a trajectory,
click it again when trajectory is long enough, to stop drawing
- 4. change color of trajectory if you wish:
change inkcolor (0.0 is black),
retrace (can only be done once)
- 5. if satisfied with the trajectory colors,
cleanup (removes all turtles leaving trajectories)
- 6. repeat steps 2-5 looking for new attractors and coloring basins
- Suggestions
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