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| 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. |
| 关键词: 非标准有限差分方法 Mackey-Glass系统 霍普夫分支 稳定性 |
| DOI： |
| 分类号:O241.81 |
| 基金项目:Supported by National Natural Science Foundation of China (11201084, 61803095) and Natural Science Foundation of Guangdong Province (2017A030313031) |
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| NUMERICAL DYNAMICS OF NONSTANDARD FINITE DIFFERENCE METHOD FOR MACKEY-GLASS SYSTEM |
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Jie-yi YAO,Qi WANG
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| Abstract: |
| 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. |
| Key words: nonstandard finite difference method Mackey-Glass system Hopf bifurcation stability |
