Results 191 to 200 of about 5,207 (226)
Some of the next articles are maybe not open access.
Remark on the Hopf Bifurcation Theorem
Mathematische Nachrichten, 2004AbstractA 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.
openaire +2 more sources
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
openaire +1 more source
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) .
openaire +1 more source
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) .
openaire +1 more source
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.
openaire +1 more source
A Hopf bifurcation with spherical symmetry
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1992The 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
openaire +4 more sources
Stochastically perturbed hopf bifurcation
International Journal of Non-Linear Mechanics, 1987A 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.
openaire +1 more source
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.
openaire +2 more sources
Computational Methods for Nonlinear Analysis of Hopf Bifurcations in Power System Models
Electric Power Systems Research, 2022Habib Wajid +2 more
exaly
Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems
Physics Reports, 2022D J W Simpson
exaly
Hopf bifurcations in dynamics of excitable systems
Ricerche Di Matematica, 2022Mónica De Angelis, De Angelis Mónica
exaly