Previous | ToC Labs: Birth, Growth, Death and Chaos. Part 1. Math Alive

Plotting Non-Linear Models

When the graph window appears (often in the upper left corner), please resize the window to get the full view of the graph. The top window shows the population vs time. The lower window plots the last iteration vs the previous iteration. P0 is the population from which the system starts at time zero. Pc gives the population at the current iteration. This is useful when the stepwise mode is on. (See below)

Enter the values r = 1, P0 = 0.1, N = 20. (The population values are rescaled so that c = 1 as described in class.) The corresponding graph of the logistic equation appears. There are two modes of operation.

  • Stepwise mode on: When the stepwise mode is on, click the [Iterate] button to successively apply the map up to a total number of N iterations.
  • Stepwise mode off: The [Plot whole curve] button will plot the entire trajectory up to time N.

The "staircase" will turn the "web" on in the lower display. For long runs, you might want to turn off the web. The clear button will clear all plots.

Now change P0 to 1.85. Repeat the plotting procedure. A second trajectory will appear in a different color on top of the first. Click on the "clear all" button to clear the screen should you want to clear.

Repeat once more, setting P0 to 0.05. Note how all three solutions, starting with low or high populations, converge on the carrying capacity.

Now change r to 1.8 and repeat, choosing several different initial populations in the allowable range (0 to 1.55, for r=1.8: see horizontal axis on lower graph window). Note how the approach to carrying capacity is now oscillatory.

If you want to clear the screen, click on the "clear all" button.

How to Print Plots

Previous | ToC Last Modified: August 2008