关于带有强迫项系统稳定性的研究

doi:10.7523/j.issn.2095-6134.2017.03.002

中国科学院大学学报 ›› 2017, Vol. 34 ›› Issue (3): 277-288.DOI: 10.7523/j.issn.2095-6134.2017.03.002

关于带有强迫项系统稳定性的研究

郭来刚, 陈玉福

中国科学院大学数学科学学院, 北京 100049

收稿日期:2016-07-07 修回日期:2016-11-08 发布日期:2017-05-15
通讯作者: 陈玉福,E-mail:yfchen@ucas.ac.cn
基金资助:
Supported by the National Natural Science Foundation of China (11271363)

Study on stability of systems with forced term

GUO Laigang, CHEN Yufu

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-07-07 Revised:2016-11-08 Published:2017-05-15
Supported by:
Supported by the National Natural Science Foundation of China (11271363)

摘要/Abstract

摘要： 研究带有强迫项的系统，给出微分动力系统添加强迫项使其渐进稳定的两种方法。第一种方法建立在李雅普诺夫直接法的基础上；第二种方法则是基于Hopf分叉系统稳定性研究的新方法。这个新方法的判断依据是一个由原系统系数组成的有理判别式。最后，给出关于添加强迫项的一些进一步的研究结果。

关键词: 渐近稳定性, 强迫项, 非线性动力系统, Hopf分叉

Abstract: In this work, the system with forced term is considered. Two methods for adding the forced term to the differential dynamical systems for asymptotic stability are given. The first method is based on Lyapunov's direct method, and the second method is a new method based on stability analysis of Hopf bifurcations. The new method has a discriminant which is a rational expression consisting of the coefficients in the original system. Some further researches for adding forced term are also presented.

Key words: asymptotic stability, forced term, nonlinear system, Hopf bifurcation

中图分类号:

O192

郭来刚, 陈玉福. 关于带有强迫项系统稳定性的研究[J]. 中国科学院大学学报, 2017, 34(3): 277-288.

GUO Laigang, CHEN Yufu. Study on stability of systems with forced term[J]. , 2017, 34(3): 277-288.

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关于带有强迫项系统稳定性的研究

Study on stability of systems with forced term

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