| Автор | Sofia B S D Castro |
| Дата выпуска | 1997-03-01 |
| dc.description | For a steady-state mode interaction problem with symmetry Golubitsky, Stewart and Schaeffer (1988 Singularities and Groups in Bifurcation Theory vol II (New York: Springer) ch XIX) prove that there are parameter values for which a Hopf bifurcation occurs along a mixed-mode branch. The author has proved that it is always so in mode interaction problems with symmetry (Castro S B S D 1995 Mode interactions with symmetry Dyn. Stability Syst. 10 13 - 31). In this work, we are concerned with what happens to the limit cycle arising from this Hopf bifurcation. We find that, for certain parameter values, it vanishes through a homoclinic connection. To prove this, we use Melnikov theory since the equations under study are a perturbation of Hamiltonian equations. This completes the bifurcation diagrams in Golubitsky et al (above). |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | The disappearance of the limit cycle in a mode interaction problem with symmetry |
| Тип | paper |
| DOI | 10.1088/0951-7715/10/2/007 |
| Electronic ISSN | 1361-6544 |
| Print ISSN | 0951-7715 |
| Журнал | Nonlinearity |
| Том | 10 |
| Первая страница | 425 |
| Последняя страница | 432 |
| Аффилиация | Sofia B S D Castro; Faculdade de Economia do Porto, Rua Dr Roberto Frias, 4200 Porto, Portugal and CMAUP, Rua das Taipas 135, 4050 Porto, Portugal |
| Выпуск | 2 |
