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Attractor merging crisis in chaotic business cycles. (English) Zbl 1081.37058
The present paper shows that chaotic transitions, such as the attractor merging crisis, are a fundamental feature of nonlinear business cycles. The crisis diagram for the attractor merging crises is studied, which summarizes the system dynamics leading to the onset of crisis. The onset of an attractor merging crisis is characterized using the tools of unstable periodic orbits and their associated stable and unstable manifolds. Mathematical modelling presented in the paper of crisis can deepen our understanding of sudden major changes of economic variables often encountered in business cycles.
MSC:
37N40Dynamical systems in optimization and economics
37D45Strange attractors, chaotic dynamics
37C27Periodic orbits of vector fields and flows
91B62Growth models in economics
37C70Attractors and repellers, topological structure