Hopf bifurcation on a simple cubic lattice
UNSPECIFIED. (1999) Hopf bifurcation on a simple cubic lattice. DYNAMICS AND STABILITY OF SYSTEMS, 14 (1). pp. 3-55. ISSN 0268-1110Full text not available from this repository.
We study Hopf bifurcation for differential equations defined on the space of functions on R-3 which are triply periodic with respect to a simple (primitive) cubic lattice. The centre manifold theorem reduces the problem to a system of ordinary differential equations (ODEs) on the space (C + C)(3) and symmetric under the group (O + Z(2)(c)) + T-3. We abstract this group as the wreath product group O(2)symmetry-breaking bifurcations for wreath product groups to find (up to conjugacy) all branches of periodic solutions with maximal isotropy. The stability of these solutions is calculated. Branches of periodic solutions with sub-maximal isotropy can also exist. Some possibilities for bifurcations to heteroclinic cycles are explored.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Journal or Publication Title:||DYNAMICS AND STABILITY OF SYSTEMS|
|Number of Pages:||53|
|Page Range:||pp. 3-55|
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