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Math. Comput. Appl. 2014, 19(3), 184-193; doi:10.3390/mca19030184

Analysis and Controlling of Hopf Bifurcation for Chaotic Van Der Pol-Duffing System

1
College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
2
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
*
Author to whom correspondence should be addressed.
Published: 1 December 2014
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Abstract

Analysis and controlling of bifurcation for a class of chaotic Van der Pol- Duffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is investigated. Based on the center manifold theory and normal form reduction, the stability index of bifurcation solution is given. Linear and nonlinear washout filter feedback controllers are designed respectively to control the bifurcation critical value and the amplitude of the limit cycle. Numerical simulation results are presented to illustrate analytical results found.
Keywords: chaotic Van der Pol-Duffing system; hopf bifurcation; amplitude of limit cycle; controller chaotic Van der Pol-Duffing system; hopf bifurcation; amplitude of limit cycle; controller
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. (CC BY 4.0).

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MDPI and ACS Style

Cai, P.; Tang, J.-S.; Li, Z.-B. Analysis and Controlling of Hopf Bifurcation for Chaotic Van Der Pol-Duffing System. Math. Comput. Appl. 2014, 19, 184-193.

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