Original Paper

Nonlinear Dynamics

, Volume 67, Issue 1, pp 129-138

First online:

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

  • Juan DingAffiliated withFaculty of Science, Jiangsu University Email author 
  • , Qiang MeiAffiliated withBusiness Administration Academy, Jiangsu University
  • , Hongxing YaoAffiliated withFaculty of Science, Jiangsu University

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Abstract

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.

Keywords

Advertising model Heterogeneous expectations Adaptive control Bifurcation