Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations

Figure 8

Bifurcation diagram in black color and the scaled version of the logarithm of the modified variance in blue color (a) by changing ; (b) by changing ; the results show that the variance method increases by approaching bifurcations which alarms that a tipping point is getting close.

(a)

(b)