Homoclinic tangles in a Kaldor-like business cycle model

In this paper a nonlinear discrete-time business cycle model of Kaldor-type is considered, to illustrate particular global bifurcations which determine the appearance or disappearance of attracting and repelling closed invariant curves. Such bifurcations sequences, which involve homoclinic tangencies and transversal intersection of the stable and unstable manifolds of saddle cycles, may increase the complexity of the basins of attraction of multiple, coexisting attractors. Particularly, for the business cycle model examined here, such dynamic phenomena explain the co-existence of two stable steady states and an attracting closed curve, with an intricate basin structure, for wide ranges of the parameters.