Results 201 to 210 of about 38,020 (248)

On the analysis of hopf bifurcations

International Journal of Engineering Science, 1983
Abstract The oscillatory instability and the family of limit cycles associated with a general autonomous dynamical system described by n nonlinear first order differential equations and an independently assignable scalar parameter are examined via an intrinsic method of harmonic analysis.
Huseyin, K., Atadan, A. S.
openaire   +1 more source

On Generalized Hopf Bifurcations

Journal of Dynamic Systems, Measurement, and Control, 1984
Two distinct degenerate Hopf bifurcation phenomena associated with autonomous lumped-parameter systems are explored in great detail via the intrinsic harmonic balancing method. It is assumed that the Hopf’s transversality condition is violated and certain other conditions prevail.
Huseyin, K., Atadan, A. S.
openaire   +2 more sources

Šil'nikov-Hopf bifurcation

Physica D: Nonlinear Phenomena, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hirschberg, P., Knobloch, E.
openaire   +2 more sources

Hopf bifurcation and the Hopf fibration

Nonlinearity, 1994
Summary: We present techniques for studying the local dynamics generated by an equivariant Hopf bifurcation. We show that under general hypothesis we can expect the formation of a branch of attracting invariant spheres with capture all the local dynamics.
Field, Mike, Swift, James W.
openaire   +1 more source

Computing Hopf Bifurcations I

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, Myers, Mark, Sturmfels, Bernd   +2 more
openaire   +1 more source

On stability at the Hamiltonian Hopf Bifurcation

Regular and Chaotic Dynamics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lerman, L. M., Markova, A. P.
openaire   +2 more sources

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
openaire   +1 more source

Turing Instabilities at Hopf Bifurcation

Journal of Nonlinear Science, 2009
A simple procedure for deriving a uniform asymptotic expansion for the limit cycle in the vicinity of the Hopf bifurcation point for a two dimensional reaction system \[ u_{t} =D_{u}\Delta u+f\left( u,v;a\right) , \] \[ v_{t} =D_{v}\Delta v+g\left( u,v;a\right) \tag{b} \] is suggested. First, an algorithm allowing reduction of the system (ref {b}) to a
Ricard, M.R., Mischler, Stéphane
openaire   +3 more sources

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.
openaire   +1 more source

Hopf bifurcation in the Lü system☆

Chaos, Solitons & Fractals, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu, Yongguang, Zhang, Suochun
openaire   +1 more source