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Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms
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Parker, M. J., Stewart, Ian and Gomes, M. G. M.. (2008) Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms. Dynamical Systems, Vol.23 (No.2). pp. 137-162. ISSN 1468-9367
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Official URL: http://dx.doi.org/10.1080/14689360601070771
Abstract
Physical systems often exhibit pattern-forming instabilities. Equivariant bifurcation theory is often used to investigate the existence and stability of spatially doubly periodic solutions with respect to the hexagonal lattice. Previous studies have focused on the six- and twelve-dimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translation-free axial planforms in the six- and twelve-dimensional representations is considered. This problem is studied via the abstract action of the symmetry group of the perturbation on the group orbit of the planform. A partial classification for the behaviour of the group orbits is obtained, showing the existence of homoclinic and heteroclinic cycles between equilibria.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Dynamical Systems |
| Publisher: | Taylor & Francis Ltd. |
| ISSN: | 1468-9367 |
| Date: | 2008 |
| Volume: | Vol.23 |
| Number: | No.2 |
| Number of Pages: | 26 |
| Page Range: | pp. 137-162 |
| Identification Number: | 10.1080/14689360601070771 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/29815 |
Data sourced from Thomson Reuters' Web of Knowledge
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