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Attractivity and Hopf bifurcation
Nonlinear Analysis: Theory, Methods & Applications, 1979NEGRINI, Piero, L. Salvadori
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HOPF Bifurcation for Periodic Systems
1985This paper concerns with the problem of Hopf bifurcation from an equilibrium position to periodic solutions, in the case of n dimensional periodic differential systems. Results about existence and uniqueness of bifurcating periodic solutions are obtained.
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On Hopf and Subharmonic Bifurcations [PDF]
, 1984 Let (λ,x) ∈ ℝ×ℝn →f(λ,x) ∈ ℝn be a given function that, for simplicity, we shall assume to be of classe C∞. We also assume that the partial derivative Dxf(λ,x) is bounded, uniformly with respect to (λ,x) ∈ ℝ × ℝn.
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Equivalence of degenerate Hopf bifurcations
Nonlinearity, 1991It is a very degenerate situation in Hopf bifurcation theory that all (bifurcating) periodic solutions occur for the parameter value of the bifurcation point. In principle such a singularity has infinite codimension. Therefore the problem of classification and equivalence of such bifurcation problems is very difficult.
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Hopf bifurcation on a square superlattice
Nonlinearity, 2001This paper concerns Hopf bifurcation equivariant under the group \(\Gamma:= D_4\ltimes T^2\), which acts \(\Gamma\)-simply on the phase space \(\mathbb{C}^8\). The problem is considered to be the centre manifold reduction of an evolution equation, invariant under the Euclidean group of planar translations, rotations and reflections, where the solutions
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2011
Jusqu’a present, nous avons etudie des bifurcations stationnaires correspondant a des changements de solutions stationnaires. Ce chapitre decrit quelques exemples de systemes non lineaires presentant des bifurcations de Hopf, du nom de l’astronome mathematicien autrichien Eberhard Frederich Ferdinand Hopf (1902–1983), caracteristiques d’une transition ...
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Jusqu’a present, nous avons etudie des bifurcations stationnaires correspondant a des changements de solutions stationnaires. Ce chapitre decrit quelques exemples de systemes non lineaires presentant des bifurcations de Hopf, du nom de l’astronome mathematicien autrichien Eberhard Frederich Ferdinand Hopf (1902–1983), caracteristiques d’une transition ...
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2014
In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter.
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In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter.
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2014
The final bifurcation of codimension 2 is characterized by the intersection of 2 curves of Poincare-Andronov-Hopf points on a two-dimensional surface of equilibria. As we shall see, the drift direction at the Hopf lines play an important role. In the case of a parameter-dependent fixed line of equilibria, drifts at both Hopf-lines can be opposite and ...
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The final bifurcation of codimension 2 is characterized by the intersection of 2 curves of Poincare-Andronov-Hopf points on a two-dimensional surface of equilibria. As we shall see, the drift direction at the Hopf lines play an important role. In the case of a parameter-dependent fixed line of equilibria, drifts at both Hopf-lines can be opposite and ...
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