具有网络外部性的软件市场的混沌动力学  

Chaotic Dynamics in the Software Market with Network Externalities

作　　者：刘翠 周伟[1] LIU Cui;ZHOU Wei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《兰州交通大学学报》2021年第1期120-126,共7页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(61364001);兰州交通大学青年基金(2015029);甘肃省高等学校科研项目(2015B-047)。

摘　　要：针对具有网络外部性的软件市场,构建了基于离散时间的完全垄断市场演化模型,利用动态经济学理论分析了均衡点的稳定性,并且通过数值模拟分析了系统发生分岔、混沌等复杂的动力学行为,着重借助分岔图、最大Lyapunov指数、吸引子以及吸引盆等工具讨论了各项参数的变化对低质量版本信息产品市场份额的影响.结果表明,随着低质量版本信息产品各项参数的连续变化,系统会发生倍周期分岔,甚至出现混沌,因此低质量版本信息产品的发布可能会促进高质量版本信息产品的销量,也有可能造成市场混乱.In this paper,based on discrete time periods,a complete monopoly market evolution model is built,which is aiming at the software market with network externality.The stability of the equilibrium points is analyzed by dynamic economics theory.Numerical simulation is exerted to analyze complex dynamic behaviors of the system,such as bifurcation and chaos.In particular,with the help of bifurcation diagrams,the largest Lyapunov exponents,attractors and basins of attraction,the influence of the variation of various parameters on the market share of low quality version information product is discussed in details.The results show that period-doubling bifurcation and chaos arise,especially when the parameters continuously change.So that,the release of the low quality version of the information product may promote the sales of the high quality version of the information product,and may also cause market chaos.

关 键 词：网络外部性 垄断 分岔 混沌 吸引盆 

分 类 号：O193[理学—基础数学]