Taylor–Couette problem and related topics

Balanov, Zalman; Krawcewicz, Wiesław; Rai, Bindhyachal

doi:10.1016/s1468-1218(02)00076-7

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…At the same time, this method does not allow to obtain stability results for bifurcating branches. For a detailed exposition of the equivariant degree theory and its applications, we refer to [5,7,8,9,23,24,29]). The goal of the present paper is to apply the abstract results from [4] to study equivariant Hopf bifurcation of relative equilibria/relative periodic solutions in delay differential equations (DDE) describing a system of 5 mode-locked lasers coupled in S 5 -symmetric fashion.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

2018

J. Nonlinear Var. Anal.

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The goal of this paper is to study the equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in a system of five identical passively mode-locked semiconductor lasers coupled in the S 5-equivariant fashion. Each laser is described by a delay differential model respecting a spacial S 1-symmetry. The existence of branches of relative periodic solutions together with their symmetric classification is established using the equivariant twisted S 5 × S 1-degree with one free parameter. Theoretical results are supported by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

2018

J. Nonlinear Var. Anal.

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“…[1,2,4,5,14,18,21,25,26]) provides the most effective method for a full analysis of symmetric Hopf bifurcation problems (cf. [5,6,12,18,24,34,35]). It allows to directly translate the equivariant spectral properties of the characteristic operator (associated with the system) into an algebraic invariant containing the information related to the topological nature of the occurring Hopf bifurcation, including the symmetric structure of the bifurcating branches of non-constant periodic solutions, and their multiplicities.…”

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confidence: 99%

Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations

Balanov

Farzamirad

Krawcewicz

et al. 2006

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper we apply the equivariant degree method to the Hopf bifurcation problem for a system of symmetric functional differential equations. Local Hopf bifurcation is classified by means of an equivariant topological invariant based on the symmetric properties of the characteristic operator. As examples, symmetric configurations of identical oscillators, with dihedral, tetrahedral, octahedral, and icosahedral symmetries, are analyzed.

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Equivariant Degree

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Handbook of Topological Fixed Point Theory

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Taylor–Couette problem and related topics

Cited by 7 publications

References 22 publications

Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations

Equivariant Degree

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