Results 191 to 200 of about 12,431 (232)

The Hopf Bifurcation

1985
The term Hopf bifurcation refers to a phenomenon in which a steady state of an evolution equation evolves into a periodic orbit as a bifurcation parameter is varied. The Hopf bifurcation theorem (Theorem 3.2) provides sufficient conditions for determining when this behavior occurs.
Martin Golubitsky, David G. Schaeffer
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Periodically Perturbed Hopf Bifurcation

SIAM Journal on Applied Mathematics, 1987
A 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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Remark on the Hopf Bifurcation Theorem

Mathematische Nachrichten, 2004
AbstractA simple generalization of the Hopf Bifurcation Theorem for scalar higher order ordinary differential equations is suggested. We study the degenerate case where several roots of the characteristic polynomial cross the imaginary axis at the same point for some value λ0 of the parameter λ.
Krasnosel'skii, A. M., Rachinskii, D. I.
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Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation

2008 47th IEEE Conference on Decision and Control, 2008
It 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, Fernando Verduzco Gonzalez   +1 more
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The Hopf Bifurcation

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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Anti-control of Hopf bifurcations

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2001
Summary: Bifurcation control generally means the design of a controller that is capable of modifying the bifurcation characteristics of a bifurcating nonlinear system, thereby achieving some desirable dynamical behaviors. A typical objective is to delay and/or stabilize an existing bifurcation. In this paper, we consider the problem of anti-controlling
Chen, Dong S., Wang, Hua O., Chen, Guanrong   +2 more
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On the Andronov–Hopf Bifurcation Theorem

Differential Equations, 2001
Based 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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A Hopf bifurcation with spherical symmetry

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1992
The authors consider Hopf bifurcation on a ten dimensional center manifold in a \(O(3)\)-symmetric system. The main hypothesis is that the representation on the critical modes is given by the representation on \(V_ 5\oplus V_ 5\), the sum of two copies of the absolutely irreducible representations of \(O(3)\) on the spherical harmonics of order two ...
HAAF, H, ROBERTS, M, STEWART, I
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Stochastically perturbed hopf bifurcation

International Journal of Non-Linear Mechanics, 1987
A two-dimensional system of differential equations \[ \frac{dy}{dt}=F(y,\sigma)+\epsilon^{1/2}[A_ 1(\sigma)f(t)+A_ 2(\sigma)g(t)]y \] is considered where F is a vector function analytic in y and \(\sigma\), \(\sigma\) is a real-valued parameter, \(A_ 1(\sigma)\), \(A_ 2(\sigma)\) are \(2\times 2\)-matrices which depend only on \(\sigma\), f(t), g(t ...
Sri Namachchivaya, N., Ariaratnam, S. T.
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HOPF Bifurcation for Periodic Systems

1985
This 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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