Mechanics → Introduction to Nonlinear Dynamics and Chaos → Logistic Map
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Logistic Map

A simple example of chaos:

$$ x_{n+1} = r x_n (1 - x_n) $$

Behavior

  • Small $r \to \text{stable}$
  • Larger $r \to \text{oscillations}$
  • High $r \to \text{chaos}$