Guaranteed estimates for the length of branches of periodic orbits for equivariant Hopf bifurcation

0534405 - MÚ 2021 RIV SG eng J - Journal Article
Hooton, Edward - Balanov, Z. - Rachinskii, D.
Guaranteed estimates for the length of branches of periodic orbits for equivariant Hopf bifurcation.
International Journal of Bifurcation and Chaos. Roč. 30, č. 13 (2020), č. článku 2050198. ISSN 0218-1274. E-ISSN 1793-6551
Institutional support: RVO:67985840
Keywords : global Hopf bifurcation * equivariant system * S1-degree * spatiotemporal symmetry
OECD category: Pure mathematics
Impact factor: 2.836, year: 2020
Method of publishing: Limited access
https://doi.org/10.1142/S0218127420501989

Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the assumption that the nonlinear terms satisfy a linear estimate in a ball. If the estimate is global, then the branch is unbounded. The results are formulated in an equivariant setting where the system can have multiple branches of periodic orbits characterized by different groups of symmetries. The nonlocal analysis is based on the equivariant degree method, which allows us to handle both generic and degenerate Hopf bifurcations. This is illustrated by examples.
Permanent Link: http://hdl.handle.net/11104/0312604