Figure 1.

(a) The map in Eq. (7) with z = 2 and u = −0.005 (red), two trajectories are shown with x₀ < 0 and x₀ > 0 (blue). The insets show the time dependence of these trajectories that obey Eq. (10). (b) Rank-order statistics for the occurrence of forest fires (blue dots) from Ref. [13]. They are reproduced by the smooth curve from Eq. (11) with α = 2 and ${\mathcal{N}}^{-1}=-u$ (red). The inset shows the same data (blue) plotted in ${\ln }_{{\alpha }^{\prime }}(p_k/p_{\min })$ scale, p_k = 1/N(k) and α^′ = 0. The straight line is the corresponding plot of Eq. (12) (red) and evidences the extensivity of the entropy in Eq. (13). See text for details.