A note on linear differential equations with periodic coefficients

被引：4

作者：

Grau, Maite ^{[1
]}

Peralta-Salas, Daniel ^{[2
]}

机构：

[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain

[2] Univ Carlos III Madrid, Dept Matemat, Madrid 28911, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 7-8期

关键词：

Linear differential equations; Characteristic multipliers; Hyperbolicity; Limit cycles; STABILITY; SYSTEMS;

D O I：

10.1016/j.na.2009.01.199

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider linear homogeneous differential equations of the form (x) over dot = A(t)x where A(t) is a square matrix of C-1, real and T-periodic functions, with T > 0. We give several criteria on the matrix A(t) to prove the asymptotic stability of the trivial solution to equation (x) over dot = A(t)x. These criteria allow us to show that any finite configuration of cycles in R-n can be realized as hyperbolic limit cycles of a polynomial vector field. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：3197 / 3202

页数：6

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