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Examples of forced symmetry-breaking to homoclinic cycles in three-dimensional Euclidean-invariant systems
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Parker, M. J., Stewart, Ian and Gomes, M. G. M. (2008) Examples of forced symmetry-breaking to homoclinic cycles in three-dimensional Euclidean-invariant systems. International Journal of Bifurcation and Chaos, Vol.18 (No.1). pp. 83-107. doi:10.1142/S0218127408020161
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Official URL: http://dx.doi.org/10.1142/S0218127408020161
Abstract
We study perturbations of cubic planforms, proving there exists perturbations with homoclinic cycles between persistent steady states. Our results do not depend on the representation of the symmetry group of the lattice, and are thus quite general. .
The problem is studied using group theory rather than direct methods. We use the abstract action of the symmetry group of the perturbation on the group orbit to determine the existence of zero- and one-dimensional flow-invariant subspaces. The residual symmetry of the perturbation constrains the flows on these subspaces and, in certain cases, homoclinic cycles are guaranteed to exist.
Cubic planforms are physically interesting due to their relevance to certain physical systems. Applications to reaction-diffusion systems, nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction are discussed.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Chaotic behavior in systems, Euclidean algorithm, Bifurcation theory | ||||
| Journal or Publication Title: | International Journal of Bifurcation and Chaos | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 0218-1274 | ||||
| Official Date: | January 2008 | ||||
| Dates: |
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| Volume: | Vol.18 | ||||
| Number: | No.1 | ||||
| Number of Pages: | 25 | ||||
| Page Range: | pp. 83-107 | ||||
| DOI: | 10.1142/S0218127408020161 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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