4. Chaotic applications

Applications such as the (2) equation can also exhibit chaotic behavior. The most classic example is the logistic parabola depending on a variable x and a parameter µ.

We will introduce this equation by studying the behaviour of an isolated insect population on an island. The population x _{j + 1} of insects in summer (j + 1) depends, in a simple model, on the population x _j in summer j, according to the relationship :