摘要
本文研究了Mackey-Glass系统的数值动力性问题.利用非标准有限差分方法和离散系统的分支理论,证明了随着时间延迟的增加,在正不动点处产生了一系列霍普夫分支.同时给出了在正平衡点处霍普夫分支存在的参数条件.最后,给出了一些检验文中结论有效性的数值例子.非标准有限差分方法便于构造,运算量小,适用于非线性系统的分支分析,推广了文献中的结果.
This paper deals with the numerical dynamics for Mackey-Glass system.By using the nonstandard finite difference method and bifurcation theory of discrete systems,we prove that a series of Hopf bifurcation appear at the positive fixed point with the increase of time delay.At the same time,the parameter conditions for the existence of Hopf bifurcations at positive equilibrium point are given.Finally,we provide some numerical examples to illustrate the effectiveness of our results.The nonstandard finite difference method is easy to construct and has less computation.It is suitable for the bifurcation analysis of nonlinear systems and extends the results in the literature.
作者
姚洁怡
王琦
YAO Jie-yi;WANG Qi(School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510006,China)
出处
《数学杂志》
2022年第1期63-72,共10页
Journal of Mathematics
基金
Supported by National Natural Science Foundation of China (11201084,61803095)
Natural Science Foundation of Guangdong Province (2017A030313031)。