随机经济模型的Hopf分岔研究  

Hopf bifurcation of stochastic economic model

作　　者：彭建奎 张莉 安新磊[3] 杨兆兰 PENG Jiankui;ZHANG Li;AN Xinlei;YANG Zhaolan(School of Education,Lanzhou University of Arts and Science,Lanzhou 730010,China;Basic Courses Department,Lanzhou Institute of Technology,Lanzhou 730050,China;School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州文理学院教育学院,兰州730010 [2]兰州工业学院基础学科部,兰州730050 [3]兰州交通大学数理学院,兰州730070

出　　处：《延边大学学报（自然科学版）》2022年第3期205-212,共8页Journal of Yanbian University（Natural Science Edition）

基　　金：甘肃省高等学校创新基金(2022A-172);甘肃省自然科学基金(20CX9ZA076);国家自然科学基金(11962012)。

摘　　要：运用非线性动力学理论对带有随机参数的微分方程经济模型的Hopf分岔进行了研究.首先,选择拱形分布的随机变量并利用Chebyshev正交多项式逼近法将经济模型转化为确定性等价系统.然后,运用Hopf分岔定理与Lyapunov系数相关理论研究了系统的稳定性和Hopf分岔的存在性等,结果显示随机参数对系统的稳定性具有很大影响.最后,运用数值仿真验证了系统具有平衡点渐近稳定性,并存在Hopf分岔现象.该研究结果可为调控和保持金融市场稳定提供理论参考.Hopf bifurcation in the differential equation economic model with stochastic parameters is studied by nonlinear dynamics theory.Firstly,the economic model is transformed into a deterministic equivalent system using Chebyshev orthogonal polynomial approximation theory.Then,the stability of the system and the existence of Hopf bifurcation are studied by the Hopf bifurcation theorem and Lyapunov coefficient correlation theory,and it is found that the random parameters have a great influence on the stability.Finally,numerical simulation shows that the system has asymptotic stability and Hopf bifurcation.The research results can provide theoretical reference for the financial market stability regulation and maintaining.

关 键 词：HOPF分岔 正交多项式 经济模型 Lyapunov系数 

分 类 号：O322[理学—一般力学与力学基础]