Chaotic dynamic properties for an advertising model in duopoly market
双头垄断市场中广告模型的混沌动态特性

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.