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

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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