|Figure 1: A Business Cycle|
|Figure 2: National Output in The Business Cycle|
By the way, my evidence for the existence of a limit cycle with saddle-point stability consists of graphical representations like these. I have not yet been able to find a sequence of (presumably 62) points that exactly repeat. Each of these points along such a limit cycle would have a corresponding stable and unstable set. And the possibility arises of these stable and unstable sets intertwining in a complicated fashion away from the limit cycle. The title of Agliari et al.'s paper refers to such homoclinic tangles of the stable and unstable sets of points along a limit cycle with saddle point stability. The title is not referring to a homoclinic bifurcation of a limit point at the origin, albeit they point out that bifurcation also.
- Agliari, A.; R. Dieci; and L. Gardini (2007). "Homoclinic Tangles in a Kaldor-Like Business Cycle Model", Journal of Economic Behavior & Organization. V. 62: 324-347.