The Bifurcation of Two Invariant Closed Curves in a Discrete Model

Figure 1

The stability of equilibrium point in plane. (a) The stability of and the two curves denote the flip bifurcation manifolds and divide the plane into four regions with different stability of . The intersections denote the strong 1 : 2 resonance. (b) The stability of . (c) The stability of . (d) The stability of . exists when values are underneath curve. N-S curve denotes the Neimark-Sacker manifold. The N-S curve and flip curve divide the plane into three regions with different stability of .

(a)

(b)

(c)

(d)