The Library
Examples or forced symmetry-breaking to heteroclinic cycles and networks in three-dimensional euclidean-invariant systems
Tools
Parker, M. J., Gomes, M. G. M. and Stewart, Ian (2009) Examples or forced symmetry-breaking to heteroclinic cycles and networks in three-dimensional euclidean-invariant systems. International Journal of Bifurcation and Chaos, Vol.19 (No.5). pp. 1655-1678. doi:10.1142/S0218127409023767 ISSN 0218-1274.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1142/S0218127409023767
Abstract
In [Parker et al., 2008a] group theory was employed to prove the existence of homoclinic cycles in forced symmetry-breaking of simple (SC), face-centered (FCC), and body-centered (BCC) cubic planforms. In this paper we extend this classification demonstrating that more elaborate heteroclinic cycles and networks can arise through the same process. Our methods naturally generate graphs that represent possible heteroclinic cycles and networks. The results do not depend on the representation of the symmetry group and are thus quite general.
This study is motivated by pattern formation in three dimensions which occur in reaction diffusion systems, certain nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction. This work extends previous work by Parker et al. [2006, 2008a, 2008b] and Hou and Golubitsky [1997].
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics Q Science |
||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | International Journal of Bifurcation and Chaos | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-1274 | ||||
Official Date: | May 2009 | ||||
Dates: |
|
||||
Volume: | Vol.19 | ||||
Number: | No.5 | ||||
Number of Pages: | 24 | ||||
Page Range: | pp. 1655-1678 | ||||
DOI: | 10.1142/S0218127409023767 | ||||
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
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |