Complex Dynamics Analysis And Control For A Duopoly Advertising Model

On the basis of the dynamic cournot game model, we have built the duopoly advertising model with nonlinear cost. On this basis, we point out the stable region of Nash equilibrium and its influencing factors by analyzing the evolution process of the improved model. We discover when enterprise accelerates the adjustment speed of the output quantity in advertisement and increases the market demand of the advertisement unit in order to achieve initial advantage, it leads to instability of systems and makes the systems sink into the chaotic state. In addition, we have pointed out the makers of chaos can not definitely gain more advantage than its competitor while entering Chaos.Applying straight-line stabilization method to a duopoly advertising model with bounded rationality, we gain a duopoly advertising model with bounded rationality. Then we study the enterprise control the system in different time point. One is stabilizing chaos in the neighborhood of Nash equilibrium, the other is suppressing chaos in the farther point from Nash equilibrium. Through theoretical analysis and numerical simulation, we discover that the initial cost of control chaos and the control result depend on the time of the enterprise applying straight-line stabilization method to system and the value of the gain matrix k and at the same of control point, the control result is closely related to the values of k. Meanwhile, pointing out the enterprise in the chaos will can obtain the better control result than others, if it control chaos in the neighborhood of Nash equilibrium or two sides.Considering a delayed duopoly advertising model with bounded rationality and then studying the effects of the delayed decision, we analyse the stability of the model. On this basis, through theoretical analysis and numerical simulation, we discover that the enterprise with delayed decision can not definitely gain more advantages than its competitor does in terms of accumulated profit they gain. It mainly depends on the weights of delayed variable and the time chosen to apply the delayed decision. Studying the relation between the weights of delayed variable and the region of...