Results 181 to 190 of about 12,431 (232)

On anticontrol of Hopf bifurcations

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002
The control of the amplitude of the oscillations in an underactuated mechanical system is treated. Two different procedures for the design of the controller are proposed. One is based on Hopf bifurcation theory, and the other is derived from considerations about the system's energy.
Diego M. Alonso, Eduardo E. Paolini, Jorge L. Moiola   +2 more
openaire   +1 more source

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

On the control of Hopf bifurcations

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002
Linear and quadratic normal forms of nonlinear systems with a pair of imaginary uncontrollable modes are derived. Based on the normal form, formulae of feedbacks are found to control the bifurcation of the system. The Hopf bifurcation cannot be removed from the closed-loop system, because the imaginary eigenvalues are uncontrollable.
Boumediene Hamzi, Wei Kang 0001, Jean-Pierre Barbot   +2 more
openaire   +1 more source

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

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

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

Analysis and Control of Hopf Bifurcations

SIAM Journal on Control and Optimization, 2004
Summary: In this paper, control systems with two uncontrollable modes on the imaginary axis are studied. The main contributions include the local orientation control of periodic solutions and center manifolds, the quadratic normal form of systems with two imaginary uncontrollable modes, the stabilization of the Hopf bifurcation by state feedback, and ...
Boumediene Hamzi, Wei Kang 0001, Jean-Pierre Barbot   +2 more
openaire   +2 more sources

Hopf bifurcation and Hopf hopping in recurrent nets

IEEE International Conference on Neural Networks, 2002
Some aspects of the learning dynamics of recurrent neural networks are discussed. It is shown that as a two-unit fully recurrent network is trained to oscillate, the learning process brings the network to a point where a small change in any one of the weights can push the network through a Hopf bifurcation to create stable oscillation.
Fu-Sheng Tsung, Garrison W. Cottrell
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