关于带有强迫项系统稳定性的研究  

Study on stability of systems with forced term

作　　者：郭来刚 陈玉福[1] 

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2017年第3期277-288,共12页Journal of University of Chinese Academy of Sciences

基　　金：Supported by the National Natural Science Foundation of China （11271363 ）

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。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.

关 键 词：渐近稳定性 强迫项 非线性动力系统 HOPF分叉 

分 类 号：O192[理学—数学]