Results 181 to 190 of about 5,207 (226)
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On the control of Hopf bifurcations
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002Linear 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 +2 more
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On the analysis of hopf bifurcations
International Journal of Engineering Science, 1983Abstract 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.
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On Generalized Hopf Bifurcations
Journal of Dynamic Systems, Measurement, and Control, 1984Two 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.
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Hopf bifurcation and the Hopf fibration
Nonlinearity, 1994Summary: 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.
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Turing Instabilities at Hopf Bifurcation
Journal of Nonlinear Science, 2009A 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
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Analysis and Control of Hopf Bifurcations
SIAM Journal on Control and Optimization, 2004Summary: 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 +2 more
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Hopf bifurcation and Hopf hopping in recurrent nets
IEEE International Conference on Neural Networks, 2002Some 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
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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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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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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, 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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