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Equivariant degree method for analysis of Hopf bifurcation of relative periodic solutions: Case study of a ring of oscillators.
- Source :
-
Journal of Differential Equations . Nov2018, Vol. 265 Issue 9, p4530-4574. 45p. - Publication Year :
- 2018
-
Abstract
- Abstract The goal of this paper is to develop the Equivariant Degree based method for studying relative periodic solutions in the setiings with lack of smoothness and/or genericity. In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting Γ × S 1 -spatial symmetries. The existence of branches of relative periodic solutions together with their symmetric classification is established using the equivariant twisted Γ × S 1 -degree with one free parameter. As a case study, we consider a delay differential model of coupled identical passively mode-locked semiconductor lasers with the dihedral symmetry group Γ = D 8 ; and, a system of hysterestic electro-mechanical oscillators coupled in the same symmetric fashion. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 265
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 132868694
- Full Text :
- https://doi.org/10.1016/j.jde.2018.06.014