中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4748-4753.doi: 10.1088/1674-1056/18/11/024

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Amplitude control of limit cycle in a van der Pol Duffing system

欧阳克俭1, 唐驾时2, 梁翠香2   

  1. (1)College of Civil Engineering, Hunan University, Changsha 410082, China; (2)College of Mechanics and Aerospace, Hunan University, Changsha 410082, China
  • 收稿日期:2009-02-14 修回日期:2009-04-04 出版日期:2009-11-20 发布日期:2009-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10672053).

Amplitude control of limit cycle in a van der Pol--Duffing system

Ouyang Ke-Jian(欧阳克俭)a)†, Tang Jia-Shi(唐驾时)b), and Liang Cui-Xiang(梁翠香)b)   

  1. a College of Civil Engineering, Hunan University, Changsha 410082, China; b College of Mechanics and Aerospace, Hunan University, Changsha 410082, China
  • Received:2009-02-14 Revised:2009-04-04 Online:2009-11-20 Published:2009-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10672053).

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摘要： This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol--Duffing system. The controlling parameters for the appearance of Hopf bifurcation are given by the Routh--Hurwitz criteria. Noticeably, numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol--Duffing system but also of the strongly nonlinear van der Pol--Duffing system. In particular, the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters. Gain-amplitude curves of controlled systems are also drawn.

Abstract: This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol--Duffing system. The controlling parameters for the appearance of Hopf bifurcation are given by the Routh--Hurwitz criteria. Noticeably, numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol--Duffing system but also of the strongly nonlinear van der Pol--Duffing system. In particular, the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters. Gain-amplitude curves of controlled systems are also drawn.

Key words: bifurcation control, limit cycle, Hopf bifurcation, van der Pol--Duffing system

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Pq (Numerical simulations of chaotic systems) 02.60.Cb (Numerical simulation; solution of equations)