The logistic map is a simple second-order function on the unit interval: $\displaystyle x_{n+1} = r x_n (1-x_n) \,$, where ${x_n}$ is the variable value at stage {n} and {r} is the “growth rate”.
For ${1 \le r \le 4}$, the map sends the unit interval [0,1] into itself. It is a simple nonlinear difference equation, whose solutions exhibit both regular and erratic behaviour, and it is often used to demonstrate some important characteristics of chaotic motion.
It describes behaviour found in a wide range of disciplines: physics, engineering, economics and biology.
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