The graph shows the Lyapunov exponent L(c) = lim_{n} (1/n) log| f'_{c}^{n}(x) | of the Logistic map f_{c}(x) = c x (1-x) and f^{n}(x) = f (f^{(n-1)}(x)). The graph of the function L(c) is plotted for values of c between 3 and 4. A positive Lypunov exponent (for example at c=4) indicates chaotic behavior = sensitive dependence on initial conditions of the map. |