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A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation
| Content Provider | Scilit |
|---|---|
| Author | Algaba, Antonio Freire, E. Gamero, Estanislao Rodríguez-Luis, Alejandro José |
| Copyright Year | 1999 |
| Description | Journal: Nonlinearity A codimension-three unfolding for the$ _{2}$-symmetric Hopf-pitchfork bifurcation, in the presence of an additional nonlinear degeneracy, is analysed. Up to ten distinct topological equivalence classes for the unfolding are found. A rich variety of dynamical and bifurcation behaviours is pointed out. Beyond the bifurcations present in the nondegenerate case, we show that the following bifurcations appear locally: Takens - Bogdanov of periodic orbits, degenerate pitchfork of periodic orbits, and global connections involving equilibria and/or periodic orbits. The local results achieved, extended by means of numerical continuation methods, are used to understand the dynamics of a modified van der Pol - Duffing electronic oscillator, for a certain range of the parameters. |
| Related Links | http://iopscience.iop.org/article/10.1088/0951-7715/12/4/324/pdf |
| Ending Page | 1206 |
| Page Count | 30 |
| Starting Page | 1177 |
| ISSN | 09517715 |
| e-ISSN | 13616544 |
| DOI | 10.1088/0951-7715/12/4/324 |
| Journal | Nonlinearity |
| Issue Number | 4 |
| Volume Number | 12 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Nonlinearity |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics |
