Hopf bifurcation on a simple cubic lattice

• Type: Article in International Scientific Journal
• Date: 1999

Authors

dias, aps (Author) FCUP; stewart, i (Author) Other

Journal

Title: Dynamics and Stability of Systems

Vol. 14

Pages: 3-55

ISSN: 0268-1110

Publisher: Oxford University Press

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 5 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-4YZ

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 53