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Chaotic attractors, chaotic saddles, and fractal basin boundaries: Goodwin’s nonlinear accelerator model reconsidered. (English) Zbl 1016.37052
Summary: Goodwin’s 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.

MSC:
37N40 Dynamical systems in optimization and economics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
91B62 Economic growth models
Software:
Dynamics
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