Nonlinear Dynamics

, Volume 67, Issue 1, pp 129–138

Dynamics and adaptive control of a Duopoly advertising model based on heterogeneous expectations


    • Faculty of ScienceJiangsu University
  • Qiang Mei
    • Business Administration AcademyJiangsu University
  • Hongxing Yao
    • Faculty of ScienceJiangsu University
Original Paper

DOI: 10.1007/s11071-011-9964-y

Cite this article as:
Ding, J., Mei, Q. & Yao, H. Nonlinear Dyn (2012) 67: 129. doi:10.1007/s11071-011-9964-y


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.


Advertising modelHeterogeneous expectationsAdaptive controlBifurcation
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© Springer Science+Business Media B.V. 2011