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A new method to control chaos in an economic system. (English) Zbl 1200.91195
Summary: In this paper, the method to control chaos by using phase space compression is applied to economic systems. Because of economic significance of state variable in economic dynamical systems, the values of state variables are positive due to capacity constraints and financial constraints, we can control chaos by adding upper bound or lower bound to state variables in economic dynamical systems, which is different from the chaos stabilization in engineering or physics systems. The knowledge about system dynamics and the exact variety of parameters are not needed in the application of this control method, so it is very convenient to apply this method. Two kinds of chaos in the dynamic duopoly output systems are stabilized in a neighborhood of an unstable fixed point by using the chaos controlling method. The results show that performance of the system is improved by controlling chaos. In practice, owing to capacity constraints, financial constraints and cautious responses to uncertainty in the world, the firm often restrains the output, advertisement expenses, research cost etc. to confine the range of these variables’ fluctuation. This shows that the decision maker uses this method unconsciously in practice.
91B55Economic dynamics
37N40Dynamical systems in optimization and economics
37N35Dynamical systems in control
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