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Hopf bifurcation with non-semisimple 1:1 resonance
| Content Provider | Scilit |
|---|---|
| Author | Gils, S. A. Van Krupa, M. Langford, W. F. |
| Copyright Year | 1990 |
| Description | Journal: Nonlinearity 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 $122^{3}$ on which the system has four different codimension-2 singularities: a Bogdanov-Takens bifurcation a $132_{2}$ symmetric cusp, a Hopf/Hopf mode interaction without strong resonance, and a steady-state/Hopf mode interaction with eigenvalues (0, i,-i). |
| Related Links | http://iopscience.iop.org/article/10.1088/0951-7715/3/3/013/pdf |
| Ending Page | 850 |
| Page Count | 26 |
| Starting Page | 825 |
| ISSN | 09517715 |
| e-ISSN | 13616544 |
| DOI | 10.1088/0951-7715/3/3/013 |
| Journal | Nonlinearity |
| Issue Number | 3 |
| Volume Number | 3 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 1990-08-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Nonlinearity Parameter Space Phase Shift Steady State Normal Form Hopf Bifurcation Three Dimensional |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics |
