一类混沌广告模型的直线控制

将参数扰动直线控制法引入到双寡头有限理性广告博弈模型中，建立了双寡头广告直线控制模型。研究两种不同情况下企业对系统进行控制，一是在NASH均衡点附近时引入直线控制，另一种是在较远的点时引入直线控制。通过理论分析和数值模拟发现，初期控制成本和控制效果依赖于企业控制点的选择和增益矩阵k的取值，在同一个控制点，控制效果与k值密切相关。同时指出对于处于混沌状态的企业，应选择在两企业的广告投入量位于NASH均衡点附近或两侧时，进行控制，将能够取得比较好的控制效果。

A Straight-Line Stabilization Method for a Kind of Chaotic Advertising Model

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 obtain the better control result than others, if it control chaos in the neighborhood of Nash equilibrium or two sides.