Nonautonomous bifurcation patterns for one-dimensional differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:234

Article

Rasmussen, Martin

关键词: nonautonomous differential equation;    linear differential equation;    attractive solution;    attractor;    repulsive solution;    repeller;    nonantonomous bifurcation theory;   

DOI  :  10.1016/j.jde.2006.11.002

来源: Elsevier

【 摘 要 】

Although, bifurcation theory of ordinary differential equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this article, two different approaches are discussed which are based on special notions of attractivity and repulsivity. Generalizations of the well-known one-dimensional transcritical and pitchfork bifurcation are obtained. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free