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Chaos in business cycles. (English) Zbl 0754.90014
Summary: The business cycle is studied in terms of the mapping $Z\sb t=\lambda Z\sb{t-1}-(\lambda+1)Z\sp 3\sb{t-1}-\sigma Y\sb{t-1}$, $Y\sb t=Z\sb{t- 1}+Y\sb{t-1}$, where the variables $Y$, $Z$ denote income and rate of income change respectively, and $\lambda$, $\sigma$ are two structural parameters. The model produces chaotic or periodic output for income differences. For small $\sigma$ 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:
 91B62 Growth models in economics 37D45 Strange attractors, chaotic dynamics
Full Text:
References:
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