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Convergence in nonautonomous linear differential equations with Kirchhoff coefficients
Systems & Control Letters ( IF 2.6 ) Pub Date : 2021-02-15 , DOI: 10.1016/j.sysconle.2021.104884
Ábel Garab , Mihály Pituk

A class of nonautonomous linear ordinary differential equations is considered. The coefficient matrices are Metzler matrices with zero column sums such that their directed graphs have a common directed spanning tree. It is shown that if the off-diagonal elements of the coefficients are uniformly positive along the common directed spanning tree, then under mild additional assumptions the convergence of the Perron vectors of the coefficient matrices implies that all solutions tend to a finite limit at infinity. The value of the limit can be expressed in terms of the initial data.



中文翻译:

具有Kirchhoff系数的非自治线性微分方程的收敛性

考虑一类非自治线性常微分方程。系数矩阵是具有零列总和的Metzler矩阵,因此它们的有向图具有公共的有向生成树。结果表明,如果系数的非对角元素沿着共同的有向生成树一致地为正,那么在温和的附加假设下,系数矩阵的Perron向量的收敛性意味着所有解都趋于无穷大。极限值可以用初始数据表示。

更新日期:2021-02-15
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