| 引用本文: | 齐 洁, 汪定伟.双头垄断市场中广告模型的混沌动态特性[J].控制理论与应用,2005,22(2):273~276.[点击复制] |
| QI Jie,WANG Ding-wei.Chaotic dynamic properties for an advertising model in duopoly market[J].Control Theory and Technology,2005,22(2):273~276.[点击复制] |
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| 双头垄断市场中广告模型的混沌动态特性 |
| Chaotic dynamic properties for an advertising model in duopoly market |
| 摘要点击 1452 全文点击 2185 投稿时间：2002-12-03 修订日期：2004-11-08 |
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| DOI编号 10.7641/j.issn.1000-8152.2005.2.020 |
| 2005,22(2):273-276 |
| 中文关键词 广告模型 混沌同步 吸引子 可行集 |
| 英文关键词 advertising model chaotic synchronization attractor feasible set |
| 基金项目 国家自然科学基金资助项目(60084003;70171056). |
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| 中文摘要 |
| 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. |
| 英文摘要 |
| 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. |