Areas of attraction for nonautonomous differential equations on finite time intervals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Giesl, Peter¹  Rasmussen, Martin² 

[1] Univ Sussex, Dept Math, Falmer BN1 9QH, E Sussex, England

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

关键词: Nonautonomous differential equation;    Finite-time dynamics;    Attractivity;    Domain of attraction;    Area of attraction;    Borg's criterion;   

DOI  :  10.1016/j.jmaa.2011.12.051

来源: Elsevier

【 摘 要 】

In this article, new concepts of (exponential) attractivity for nonautonomous differential equations on a finite time interval are introduced. Due to nonuniqueness of finite-time objects, areas of attraction are studied rather than solutions which are attractive. A sufficient and necessary condition for the existence of such areas is presented, which makes use of a time-varying Riemannian metric. Several examples illustrate the theoretical results and definitions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free