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Chaos in business cycles. (English) Zbl 0754.90014
Summary: The business cycle is studied in terms of the mapping Z t =λZ t-1 -(λ+1)Z t-1 3 -σY t-1 , Y t =Z t-1 +Y t-1 , where the variables Y, Z denote income and rate of income change respectively, and λ, σ are two structural parameters. The model produces chaotic or periodic output for income differences. For small σ income acts as a slow feedback causing bifurcations between periodic and chaotic behaviour over the cycle. Typically, transitions between prosperity and depression set in with chaos after which there follows a period halving route to order.
MSC:
91B62Growth models in economics
37D45Strange attractors, chaotic dynamics