Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations

Figure 3

Cobweb diagram of System (1) in initial condition and parameter (a) ; (b) ; (c) ; (d) ; (e) ; (f) ; by increasing parameter , the sine map changes from equilibrium points to chaos, and then increasing the parameter causes some periodic dynamics in periodic windows.

(a)

(b)

(c)

(d)

(e)

(f)