Hopf bifurcations in three coupled oscillators with internal Z(2) symmetries
UNSPECIFIED. (1998) Hopf bifurcations in three coupled oscillators with internal Z(2) symmetries. DYNAMICS AND STABILITY OF SYSTEMS, 13 (1). pp. 55-93. ISSN 0268-1110Full text not available from this repository.
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 S-3, Z(2) x S-3 or Z(2) integral S-3 equivariance with respect to an 'internal' Z(2) 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 Z(2) integral S-3 case producing some quite unexpected results.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Journal or Publication Title:||DYNAMICS AND STABILITY OF SYSTEMS|
|Publisher:||CARFAX PUBL CO|
|Number of Pages:||39|
|Page Range:||pp. 55-93|
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