梯度调整机制下量子Cournot模型的动力学分析  

Dynamics Analysis of Quantum Cournot Model with Gradient Adjustment Mechanism

作　　者：朱唯唯 ZHU Weiwei(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,甘肃兰州730070

出　　处：《洛阳理工学院学报（自然科学版）》2022年第3期81-88,共8页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

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：将量子纠缠参数引入到经典Cournot模型中,建立了梯度调整机制下的量子Cournot寡头模型。利用雅可比矩阵和Jury判据的理论知识分析了平衡点的局部稳定性,通过数值模拟对模型的局部分岔行为和多稳态运动动力学进行研究。从数值模拟所展现的研究结果来看,企业调整下一时期商品产量的速度太快会使得其量子决策进入混沌态;在量子纠缠水平确定的情况下,较高的单位成本会使得系统处于不稳定的状态。此外,量子纠缠作为使企业之间进行合作的物理参数也会影响系统的行为。In the paper,the quantum entanglement parameter is introduced into the classical Cournot model,and the quantum Cournot oligopoly model with the gradient adjustment mechanism is established.Jacobian matrix and Jury criterion are used to analyse the local stability of the equilibrium point,thus resulting in the dynamics behaviour of the model is also studied,including the local bifurcation and multi-stability motion.From the research results of the numerical simulation,the increasing of adjustment speed for enterprise can cause the system chaos.When the quantum entanglement is determined,the system will be unstable due to the high unit cost.In addition,quantum entanglement,as a physical parameter for cooperation among enterprises,will also affect the behaviour of the system.

关 键 词：量子纠缠 梯度调整机制 局部分岔 稳定性 多稳态运动 

分 类 号：O302[理学—力学] F224[经济管理—国民经济]