Phys. Lett. A 284 (2001) 99-111. doi:10.1016/S0375-9601(01)00276-6

Global bifurcations in the Takens-Bogdanov normal form with D_4 symmetry near the O(2) limit

A.M.Rucklidge
Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, Cambridge, CB3 9EW, UK

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 one would expect. This great simplification allows a quantitative description of the bifurcation sequence through which stability is transfered between invariant subspaces.

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