Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations

Yūki Naito and Mervan Pašić

International Journal of Differential Equations, 2013, vol. 2013, 1-11

Abstract:

We study a new kind of asymptotic behaviour near for the nonautonomous system of two linear differential equations: , , where the matrix-valued function has a kind of singularity at . It is called rectifiable (resp., nonrectifiable) attractivity of the zero solution, which means that as and the length of the solution curve of is finite (resp., infinite) for every . It is characterized in terms of certain asymptotic behaviour of the eigenvalues of near . Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:740980

DOI: 10.1155/2013/740980

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