考虑溢出效应的量子Cournot模型的动力学研究  

Dynamical analysis of the quantum Cournot model with spillover effects

作　　者：于红梅 YU Hongmei(School of Mathematics and Science,Lanzhou Jiaotong University,Lanzhou,Gansu 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《内江师范学院学报》2025年第2期14-20,共7页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(61863022);中国博士后科学基金项目(2017M623276)。

摘　　要：基于量子博弈论和非线性动力学理论,应用Li-Du-Massar(LMA)量子化方案,构建了一个考虑溢出效应的量子Cournot动力学模型.通过Jury判据和Jacobi矩阵分析了Nash均衡点和边界均衡点的稳定性,应用Matlab进行数值模拟,研究参数的变化对于系统稳定域的影响,并且对模型中的共存、局部和全局分岔现象进行了分析.结果表明:较小的调整速度更利于市场的稳定,纠缠参数的微小变化会导致系统发生全局和局部分岔,合理控制溢出效应参数、纠缠程度和调整速度更有利于系统的稳定.Based on quantum game theory and classical game theory,a quantum Cournot dynamics model considering spillover effect is constructed by applying Li-Du-Masser quantization scheme and introducing quantum entanglement parameters.The stability of Nash equilibrium point and boundary equilibrium point is analyzed by Jury criterion and Jacobi matrix,Matlab is applied to carry out numerical simulation to study the influence of parameter changes on the stability domain of the system,and the coexistence,local and global bifurcation phenomena in the model are analyzed,and the results show that smaller adjustment speed is more conducive to the stability of the market,and the small change of entanglement parameter will lead to the occurrence of the system’s global and local bifurcation,and reasonable control of the spillover effect parameter,the degree of entanglement and the adjustment speed is more conducive to the stability of the system.

关 键 词：量子纠缠 吸引子共存 溢出效应 稳定性 分岔 

分 类 号：O302[理学—力学] F224[经济管理—国民经济]