Global bifurcations in the Takens-Bogdanov normal form with D-4 symmetry near the O(2) limit

Authors
Rucklidge, AM
Citation
Am. Rucklidge, Global bifurcations in the Takens-Bogdanov normal form with D-4 symmetry near the O(2) limit, PHYS LETT A, 284(2-3), 2001, pp. 99-111
Citations number
24
Categorie Soggetti
Physics
Journal title
PHYSICS LETTERS A
ISSN journal
03759601 → ACNP
Volume
284
Issue
2-3
Year of publication
2001
Pages
99 - 111
Database
ISI
SICI code
0375-9601(20010604)284:2-3<99:GBITTN>2.0.ZU;2-3
Abstract
The dynamics of the normal form of the Takens-Bogdanov bifurcation with D-4 symmetry is governed by a one-dimensional map near the gluing bifurcation and near the O(2) integrable limit, rather than the three-dimensional map o ne would expect. This great simplification allows a quantitative descriptio n of the bifurcation sequence through which stability is transferred betwee n invariant subspaces. (C) 2001 Elsevier Science B.V. All rights reserved.