The Bifurcation of Two Invariant Closed Curves in a Discrete Model

Figure 2

The initial value is , (a) , the middle line denotes the equilibrium point and the equilibrium point is stable, (b) , there is a period-2 orbit, (c) , there is a period-4 orbit, and (d) the bifurcation diagram in plane, showing the process of period doubling and chaos.

(a)

(b)

(c)

(d)