Nonautonomous bifurcation patterns for one-dimensional differential equations
- 作者：Martin Rasmussen
- 关键词：Nonautonomous differential equation ; Linear differential equation ; Attractive solution ; Attractor ; Repulsive solution ; Repeller ; Nonautonomous bifurcation theory
- 刊名：Journal of Differential Equations
- 出版年：2007
- 期刊代码：74_00220396
- 类别：mt
- 出版时间：1 March 2007
- 卷：234
- 期：1
- 页码：267-288
- 文件大小：224 K
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.