Year: 2018
Author: Yancong Xu, Tianzhu Lan, Zhenxue Wei
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 1 : pp. 94–110
Abstract
Homoclinic snake always refers to the branches of homoclinic orbits near a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-$k$-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-AAM-20565
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 1 : pp. 94–110
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: round-snakes round-isolas. normal form Swift-Hohenberg equation localized patterns.