Results 171 to 180 of about 65,659 (224)
Let there be multifunctionality: Uncovering the criticality zoo of the AC-DC genetic circuit
Maretvadakethope S +5 more
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International Journal of Bifurcation and Chaos, 2007
The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold.
John Harlim, William F. Langford
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The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold.
John Harlim, William F. Langford
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On anticontrol of Hopf bifurcations
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002The 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 +2 more
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Physica D: Nonlinear Phenomena, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hirschberg, P., Knobloch, E.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hirschberg, P., Knobloch, E.
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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 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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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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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, 2004In 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, thequadratic normal form of systems with two imaginary uncontrollable modes, the stabilization of the Hopf bifurcation by state feedback, and the ...
Boumediene Hamzi +2 more
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