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| Titel: |
Hopf bifurcations in three coupled oscillators with internal [image omitted] symmetries |
| Auteur: |
Wood, David |
| Verschenen in: |
Dynamical systems |
| Paginering: | Jaargang 13 (1998) nr. 1 pagina's 55-93 |
| Jaar: |
1998 |
| Inhoud: |
We consider how internal symmetries can effect the solutions observed in three symmetrically coupled oscillators due to a symmetry-breaking Hopf bifurcation, and in particular consider three cases where the coupling terms produce [image omitted] or [image omitted] equivariance with respect to an 'Internal' [image omitted] symmetry. We do this by, first, examining the generic behaviour expected on the respective centre manifolds before interpreting these results as solution branches in systems of coupled oscillators and, finally, presenting some numerical examples. By using the standard techniques, we thus present a specific example of the more general approach of Dionne et al. in a more familiar setting, as well as carrying out additional stability calculations. It turns out that is becomes extremely important how we couple the individual oscillators with respect to the internal symmetry, with the [image omitted] case producing some quite unexpected results |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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