Chaotic attractors, chaotic saddles, and fractal basin boundaries: Goodwinʹs nonlinear accelerator model reconsidered

Goodwinʹs nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple attractors which might imply the emergence of transient chaotic motion. Straddle methods are used in the analysis of the model in order to detect compact invariant (Cantor-like) sets which are responsible for the complexity of the transient motion. Economic nonlinear models, which exhibit transient chaotic dynamics, are prevalent.