Mackey-Glass系统改进欧拉法的分支行为  

Dynamics of modified Euler method for Mackey-Glass system

作　　者：姚洁怡 王琦[1] YAO Jie-yi;WANG Qi(School of Applied Mathematics,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学应用数学学院,广东广州510520

出　　处：《陕西理工大学学报（自然科学版）》2021年第3期61-67,81,共8页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：广东省自然科学基金资助项目(2017A030313031)。

摘　　要：应用改进欧拉法研究Mackey-Glass系统的分支行为。将时滞作为参数,分析数值离散系统在正平衡点处的特征根分布情况,给出Hopf分支产生的条件,同时分析了正平衡点的稳定性。最后通过数值算例验证结果的准确性,进而说明了改进欧拉法能够保持系统的分支行为。The bifurcation behavior of Mackey-Glass system is studied by using the improved Euler method.By taking time delay as a parameter,the eigenvalue distribution of numerical discrete system at positive equilibrium point is analyzed,and the conditions for the generation of Hopf bifurcation are given.At the same time,the stability of the positive equilibrium is analyzed.At last,the accuracy of the results is verified by some numerical examples,and it is shown that the improved Euler method can preserve the bifurcation behavior of the system.

关 键 词：改进欧拉法 HOPF分支 Mackey-Glass系统 稳定性 

分 类 号：O241[理学—计算数学]