Logistic Map Applet

This applet demonstrates the logistic recurrence relation:

Wikipedia has a good article on the behaviour of the logistic map, and an in-depth mathematic analysis can be found at Wolfram Mathworld.

Running the Applet

To view this applet, you will need a recent (Java J2SE 6 or later) version of Java. Webstart will allow you download the latest version if necessary. Click on the screen shot of the applet to run the application.

Use the sliders to adjust the initial value, x₀, the recurrence coefficient λ and the number of time steps t to generate values over. You will see the behaviour become chaotic for larger values of λ

The "Graph" tab simply shows the time series of the population.

The "Spiral" tab shows the iterative behaviour of the solution, and gives some insight into why the values become periodic and chaotic as lambda increases. The red parabola is the "ideal" solution, and the blue line shows the iterative value.

The "Bifurcation" tab shows the bifurcation plot generated by plotting successive iterated values of the population against all values of λ. This plot is slow to generate as the program must perform the iterations for many lamba values to generate a good plot!