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Periodically Perturbed Hopf Bifurcation
SIAM Journal on Applied Mathematics, 1987A general two-dimensional system of differential equations with periodic parametric excitation is considered with two real parameters one of them being the amplitude of the periodic excitation. As a matter of fact, the frequency of the excitation occurs also as an additional parameter, and in this respect the paper is related to the reviewer's results [
N. Sri Namachchivaya, S. T. Ariaratnam
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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]
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 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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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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