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A Torus Bifurcation Theorem with Symmetry
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gils, S. A. Van Golubitsky, Martin |
| Copyright Year | 2004 |
| Abstract | A general theory for the study of degenerate Hopf bifurcation in the presence of symmetry has been carried out only in situations where the normal form equations decoupte into phase/amplitude equations. In this paper we prove a theorem showing that in general we expect such degeneracies to lead to secondary torus bifurcations. We then apply this theorem to the case of degenerate Hopf bifurcation with triangular (D3) symmetry, proving that in codimension two there exist regions of parameter space where two branches of asymptotically stable 2-tori coexist but where no stable periodic solutions are present. Although this study does not lead to a theory for degenerate Hopf bifurcations in the presence of symmetry, it does present examples that would have to be accounted for by any such general theory. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://people.mbi.ohio-state.edu/golubitsky.4/reprintweb-0.5/output/papers/torus_90.pdf |
| Alternate Webpage(s) | http://doc.utwente.nl/96534/1/art_10.1007_BF01057416.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Abnormal degeneration Anatomic bifurcation Bifurcation theory Coexist (image) Degenerate energy levels Existential quantification Hopf bifurcation Population Parameter Torus interconnect |
| Content Type | Text |
| Resource Type | Article |
