The discrete logistic map can be used to describe the seasonal changes of a bounded population.
The tools below allow you to explore the dynamics of the map using the computer.
On the left hand side (the Time series) you see the value of ut plotted at each time step. There are 300 time steps.
On the right hand side (the Cobweb plot) you see the value of u at time t+1 plotted against its value at the previous time step.
Move the sliders to vary the value of r and the initial point u0. Click on the "+" to give each slider a precise value.
Adapted from "Three Views of the Logistic Map" from the Wolfram Demonstrations Project by Hiroki Sayama.
The bifurcation diagram summarizes the cobweb diagram by plotting the fixed points of ut against the parameter r.
This version lets you explore and enlarge different areas of the map to show its fractal nature. As the magnification increases, it is helpful to increase the number of points that are plotted.
Adapted from "Classic Logistic Map" from the Wolfram Demonstrations Project by Robert M Lurie.