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Dynamics and adaptive control of a duopoly advertising model based on heterogeneous expectations. (English) Zbl 1242.91080
Summary: This paper discusses a duopoly advertising model based on heterogeneous expectations. Firstly, it points out the unstable region of Nash equilibrium and its influencing factors by analyzing the stability of the improved model. Secondly, it applies the adaptive control method to the chaos of the duopoly advertising model. The control aims are to bring this system into the instability equilibrium point by using minor disturbance of the control parameter. The result of theoretical study and numerical simulation illuminates that the method could successfully lead the chaos track to low cycle track. Moreover, scope of the convergent condition and control intensity are given.

MSC:
91B26Market models (auctions, bargaining, bidding, selling, etc.)
91B62Growth models in economics
93C40Adaptive control systems
37N40Dynamical systems in optimization and economics
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References:
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