Examples or forced symmetry-breaking to heteroclinic cycles and networks in three-dimensional euclidean-invariant systems
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. ISSN 0218-1274Full text not available from this repository.
Official URL: http://dx.doi.org/10.1142/S0218127409023767
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 .
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||International Journal of Bifurcation and Chaos|
|Publisher:||World Scientific Publishing Co. Pte. Ltd.|
|Official Date:||May 2009|
|Number of Pages:||24|
|Page Range:||pp. 1655-1678|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC)|
Actions (login required)