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SIAM Journal on Numerical Analysis, 1997
Summary: This paper addresses the problems of detecting Hopf bifurcations in systems of ordinary differential equations and following curves of Hopf points in two-parameter families of vector fields. The established approach to this problem relies upon augmenting the equilibrium condition so that a Hopf bifurcation occurs at an isolated, regular point ...
Guckenheimer, John +2 more
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Summary: This paper addresses the problems of detecting Hopf bifurcations in systems of ordinary differential equations and following curves of Hopf points in two-parameter families of vector fields. The established approach to this problem relies upon augmenting the equilibrium condition so that a Hopf bifurcation occurs at an isolated, regular point ...
Guckenheimer, John +2 more
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Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation
2008 47th IEEE Conference on Decision and Control, 2008It is a well-known result that in a versal deformation of the Takens-Bogdanov bifurcation is possible to find dynamical systems that undergo saddle-node, homoclinic and Hopf bifurcations. In this document a nonlinear control system in the plane is considered, whose nominal vector field undergoes the Takens-Bogdanov bifurcation, and then the idea is to ...
Francisco Armando Carrillo Navarro +1 more
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On stability at the Hamiltonian Hopf Bifurcation
Regular and Chaotic Dynamics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lerman, L. M., Markova, A. P.
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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 [
Sri Namachchivaya, N., Ariaratnam, S. T.
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1979
Let X = Σ Xi∂i = Σ piξi∂i be a vectorfield on Δ. X is a function from Δ to RI. We define the Hessian of X at p, HPX: Tp Δ × Tp Δ → R to be the bilinear form defined by: $$ {H_P}X\left( {{Y^1}{Y^2}} \right) = {\left( {{d_P}X\left( {{Y^1}} \right),{Y^2}} \right)_P}. $$ (1.1) .
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Let X = Σ Xi∂i = Σ piξi∂i be a vectorfield on Δ. X is a function from Δ to RI. We define the Hessian of X at p, HPX: Tp Δ × Tp Δ → R to be the bilinear form defined by: $$ {H_P}X\left( {{Y^1}{Y^2}} \right) = {\left( {{d_P}X\left( {{Y^1}} \right),{Y^2}} \right)_P}. $$ (1.1) .
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On the Andronov–Hopf Bifurcation Theorem
Differential Equations, 2001Based on the introduced notion of a 2-regular nonlinear mapping at a singular point, the author suggests a new proof of the known Andronov-Hopf bifurcation theorem.
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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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Anti-control of Hopf bifurcation for high-dimensional chaotic system with coexisting attractors
Nonlinear Dynamics, 2022Dechang Pi, Erxi Zhu
exaly
On Hopf bifurcation and control for a delay systems
Applied Mathematics and Computation, 2020Xiangyong Chen +2 more
exaly