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Mathematical Problems in Engineering
Volume 2015, Article ID 584954, 10 pages
Research Article

Parametric Controller Design of Hopf Bifurcation System

School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611131, China

Received 11 September 2015; Accepted 17 December 2015

Academic Editor: Stefano Lenci

Copyright © 2015 Jinbo Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A general parametric controller design method is proposed for Hopf bifurcation of nonlinear dynamic system. This method does not increase the dimension of the system. Compared with the existing methods, the controller designed by this method has a lower controller order and a simpler structure, and it does not contain equilibrium points. The method keeps equilibrium of the origin system unchanged. Symbolic computation is used to deduce the constraints of controller, and cylindrical algebraic decomposition is used to find the stability parameter regions in parameter space of controller. The method is then employed for Hopf bifurcation control. Taking Lorenz system as an example, the controller design steps of the method and numerical simulations are discussed. Computer simulation results are presented to confirm the analytical predictions.