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Hopf bifurcation with non-semisimple 1:1 resonance
Gils van, S.A. and Krupa, M. and Langford, W.F. (1990) Hopf bifurcation with non-semisimple 1:1 resonance. Nonlinearity, 3 (3). p. 825. ISSN 0951-7715
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| Abstract: | A generalised Hopf bifurcation, corresponding to non-semisimple double imaginary eigenvalues (case of 1:1 resonance), is analysed using a normal form approach. This bifurcation has linear codimension-3, and a centre subspace of dimension 4. The four-dimensional normal form is reduced to a three-dimensional system, which is normal to the group orbits of a phase-shift symmetry. There may exist 0, 1 or 2 small-amplitude periodic solutions. Invariant 2-tori of quasiperiodic solutions bifurcate from these periodic solutions. The authors locate one-dimensional varieties in the parameter space 1223 on which the system has four different codimension-2 singularities: a Bogdanov-Takens bifurcation a 1322 symmetric cusp, a Hopf/Hopf mode interaction without strong resonance, and a steady-state/Hopf mode interaction with eigenvalues (0, i,-i). |
| Item Type: | Article |
| Copyright: | IOP |
| Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |
| Research Group: | |
| Link to this item: | http://purl.utwente.nl/publications/60648 |
| Official URL: | http://dx.doi.org/10.1088/0951-7715/3/3/013 |
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