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The following movies show what happens as the parameter b changes, while A and c are fixed at A = 0.45 and c = 0.1, respectively. There is a smooth invariant circle of saddle type, and one side of its unstable manifold is particularly interesting. The circle of saddle type is shown in green, its stable manifold is blue, and its unstable manifold is red. Attractors are shown in yellow.

	For b = 0.9 the unstable manifold accumulates on a smooth attracting invariant circle. The stable manifold forms the boundary of the basin of attraction (212K).
	For b = 1.0 the unstable manifold intersects the stable manifold. Note that the dynamics flips the two sides of the stable manifold, so that the homoclinic intersections involve both sides. The attractor seems smooth and persists after the homoclinic tangency (210K).
	For b = 1.05 the attracting invariant circle is still smooth, but is developing peaks that point to the stable manifold of the circle of saddle type (219K).
	For b = 1.073752 the attractor disappears, because it touches its own basin boundary. Note that the stable manifold of the circle of saddle type is not the basin boundary of the attractor anymore. However, this manifold serves as an outer approximation (333K).
	For b = 1.1 the attractor is gone (392K).

Next: A in [0.37, 0.404] Up:The bifurcation diagram