摘要
提出了一个二维离散动态广告模型,描述了两强垄断的市场中,由广告竞争引起市场份额的动态变化.在一定的参数下,对称的动态模型在二维相空间中将发生混沌同步,采用横向Lyapunov指数判定了模型的同步稳定性.定义了使模型具有经济意义的可行集,通过理论分析和数值仿真相结合的方法得到可行集的边界.通过对模型的同胚变换可得到:如果对角线上的混沌吸引子在垂直于对角线方向上局部稳定,那么它在可行集的范围内也全局稳定.
A two_dimensional discrete dynamic model of advertising is proposed describing the dynamics of the market share due to the advertising interaction in the duopoly market.Chaotic synchronization occurs in two_dimensional phase space under some parameters and its stability has been determined by transverse Lyapunov exponents.The feasible set is defined in which the variables' economic senses exist and boundaries of the feasible set can be obtained by using combined methods of theoretical analysis and numerical calculation.Based on the homeomorphous transformation for the model,it can be concluded that if the chaotic attractor for the diagonal is stable for the transverse small perturbation in neighborhood,it should be globally stable in the whole feasible set.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2005年第2期273-276,共4页
Control Theory & Applications
基金
国家自然科学基金资助项目(60084003
70171056).
关键词
广告模型
混沌同步
吸引子
可行集
advertising model
chaotic synchronization
attractor
feasible set
