منابع مشابه
HOPF BIFURCATION CONTROL WITH PD CONTROLLER
In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
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A large variety of passive optical systems subject to a delayed feedback have appeared in the literature and are described mathematically by the same class of scalar delay differential equations (DDEs). These equations include Ikeda DDE and their solutions are determined in terms of a control parameter distinct from the delay. We concentrate on the first Hopf bifurcation generated by a fixed de...
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We study a periodically forced system of ODEs near a point of Hopf bifurcation, where the forcing frequency ωF is near the Hopf frequency ωH and the forcing amplitude ε is small. We assume that in this system only the forcing frequency is varied and we determine all small amplitude periodic solutions of the forced system that have frequency ωF . In other words, we examine the influence of the f...
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The classical theorem of Hopf Bifurcation for the study of periodic solutions of ordinary differential equations (ODEs) at an equilibrium point has become the standard mathematical tool for reducing higher dimensional dynamical systems to lower dimensional systems, while at the same time preserving the emanating dynamics. The attraction for this tool is due to the fact that the classical Hopf t...
متن کاملThe Cusp-hopf bifurcation
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. It is based on truncated normal form equations, which have a phase-shift symmetry yielding a further reduction to a ...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2008
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1856