Non-conservative perturbations of homoclinic snaking scenarios
详细信息 查看全文
- 作者：Jü ; rgen Knobloch ; juergen.knobloch@tu-ilmenau.de" class="auth_mail" title="E-mail the corresponding author ; Martin Vielitz
- 关键词：37C29 ; 37G20 ; 37G40 ; 37J20
- 刊名：Journal of Differential Equations
- 出版年：2016
- 出版时间：5 January 2016
- 年：2016
- 卷：260
- 期：1
- 页码：517-566
- 全文大小：718 K
文摘
Homoclinic snaking refers to the continuation of homoclinic orbits to an equilibrium E near a heteroclinic cycle connecting E and a periodic orbit P. Typically homoclinic snaking appears in one-parameter families of reversible, conservative systems.
Here we discuss perturbations of this scenario which are both non-reversible and non-conservative. We treat this problem analytically in the spirit of the work [3]. The continuation of homoclinic orbits happens with respect to both the original continuation parameter 渭 and the perturbation parameter 位. The continuation curves are parametrised by the dwelling time L of the homoclinic orbit near P . It turns out that 位(L) tends to zero while the 渭 vs. L diagram displays isolas or criss-cross snaking curves in a neighbourhood of the original snakes-and-ladder structure.
In the course of our studies we adapt both Fenichel coordinates near P and the analysis of Shilnikov problems near P to the present situation.