Results 221 to 230 of about 53,456 (235)

Hopf bifurcation with constraints

Nonlinear Analysis: Theory, Methods & Applications, 1983
IN THIS study we give conditions for the existence of periodic orbits of a strongly continuous semiflow which branch off from a steady state for a certain parameter value. The semiflow is defined in a closed subset of a Banach space which contains the steady state.
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Hopf bifurcation on hemispheres

Nonlinearity, 2006
Field et al (1991 J. Nonlinear Sci. 1 201–23) consider the steady-state bifurcations of reaction–diffusion equations defined on the hemisphere with Neumann boundary conditions on the equator. We consider Hopf bifurcations for these equations. We show the effect of the hidden symmetries on spherical domains for the type of Hopf bifurcations that can ...
Stella M C Abreu, Ana Paula S. Dias
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Hopf bifurcation on a sphere

Nonlinearity, 2010
Using the general theory of Hopf bifurcation with symmetry we study here the example where the group of symmetries is O(3), the rotations and reflections of a sphere. We make some amendments to previously published lists of C-axial isotropy subgroups of O(3) × S1 and list the isotropy subgroups with four-dimensional fixed-point subspaces. We then study
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On a degenerate Hopf bifurcation

Journal of Physics A: Mathematical and Theoretical, 2010
We consider a one-parameter family of differential equations in with m ≥ 5 and a parameter e. We assume that for each e the differential equation has an equilibrium point x(e), that the Jacobian matrix fx(x(e), e) has two pairs of complex eigenvalues eαi ± i(β + eβi) + O(e2) for i = 1, 2 with α1α2β ≠ 0, and that the other eigenvalues are with ck ...
Luis Barreira, Claudia Valls, Jaume Llibre   +2 more
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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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Hopf Bifurcation with Symmetry

2002
In the previous chapter we studied the symmetry properties of time-periodic states of equivariant dynamical systems. We did not enquire how such states might arise. In this chapter we develop the theory of one of the most widespread routes to time-periodicity: Hopf bifurcation.
Martin Golubitsky, Ian Stewart
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Bifurcation de Hopf

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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Hopf bifurcations in dynamical systems

Ricerche di Matematica, 2019
The onset of instability in autonomous dynamical systems (ADS) of ordinary differential equations is investigated. Binary, ternary and quaternary ADS are taken into account. The stability frontier of the spectrum is analyzed. Conditions necessary and sufficient for the occurring of Hopf, Hopf–Steady, Double-Hopf and unsteady aperiodic bifurcations—in ...
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Attractivity and Hopf bifurcation

Nonlinear Analysis: Theory, Methods & Applications, 1979
NEGRINI, Piero, L. Salvadori
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Double-Hopf Bifurcation

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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