Periodic solutions of nonlinear equations based on extended stability theorems of nonlinear systems

被引：0

作者：

Sheikholeslam, F

Tahani, V ^{[1
]}

Zangenah, HRZ

机构：

[1] Isfahan Univ Technol, Dept Elect Engn, Esfahan, Iran

[2] Isfahan Univ Technol, Dept Math, Esfahan, Iran

来源：

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY | 2000年 / 24卷 / 01期

关键词：

nonlinear dynamical systems; stable equilibrium regions; Lyapunov direct method; Poincare-Bendixson theorem;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we first introduce the concepts of an equilibrium region and a stable equilibrium region. Then, we state and prove conditions under which a nonlinear autonomous system has a stable equilibrium region. It will be shown that these concepts and stability conditions are generalizations of the corresponding concepts of equilibrium points and asymptotical stable equilibrium points and their stability conditions. Using these conditions and Poincare-Bendixson theorem, we discuss conditions for the existence of periodic solutions in a nonlinear system of ordinary differential equations.

引用

页码：111 / 117

页数：7