Finding a stable solution of a system of nonlinearequations arising from dynamic systems

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成果类型：

期刊论文

作者：

Kelley, Carl T.*;Qi, Liqun;Tong, Xiaojiao;Yin, Hongxia

通讯作者：

Kelley, Carl T.

作者机构：

[Kelley, Carl T.] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.

[Qi, Liqun] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.

[Tong, Xiaojiao] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421002, Peoples R China.

[Yin, Hongxia] Minnesota State Univ Mankato, Dept Math & Stat, Mankato, MN 56001 USA.

[Kelley, Carl T.] N Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA.

通讯机构：

[Kelley, Carl T.] N

N Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA.

语种：

英文

关键词：

System of nonlinear equations;stable solutions;saddle-node bifurcation;Hopf bifurcation;stability functions;smoothing Newton method

期刊：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

ISSN：

1547-5816

年：

2011

卷：

期：

页码：

497-521

DOI：

10.3934/jimo.2011.7.497

基金类别：

US National Science FoundationNational Science Foundation (NSF) [DMS-0404537, DMS-0707220]; US Army Research Office [W911NF-04-1-0276, W911NF-05-1-0171]; Hong Kong Research Grant CouncilHong Kong Research Grants Council; Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [NSF10871031, NSF10671203, NSF70671001]; Natural Science united Foundation of Hunan-Hengyang [10JJ8008]

机构署名：

本校为其他机构

院系归属：

数学与统计学院

摘要：

In this paper, we present a new approach for finding a stable solution of a system of nonlinear equations arising from dynamical systems. We introduce the concept of stability functions and use this idea to construct stability solution models of several typical small signal stability problems in dynamical systems. Each model consists of a system of constrained semismooth equations. The advantage of the new models is twofold. Firstly, the stability requirement of dynamical systems is controlled by nonlinear inequalities. Secondly, the semismoothness property of the stability functions makes the...

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Finding a stable solution of a system of nonlinearequations arising from dynamic systems

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