中国物理B ›› 2008, Vol. 17 ›› Issue (1): 135-139.doi: 10.1088/1674-1056/17/1/024

• GENERAL • 上一篇    下一篇

Equilibrium points and bifurcation control of a chaotic system

梁翠香, 唐驾时   

  1. College of Mechanics and Aerospace, Hunan University, Changsha 410082, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10672053).

Equilibrium points and bifurcation control of a chaotic system

Liang Cui-Xiang(梁翠香)† and Tang Jia-Shi(唐驾时)   

  1. College of Mechanics and Aerospace, Hunan University, Changsha 410082, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10672053).

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摘要： Based on the Routh--Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.

Abstract: Based on the Routh--Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.

Key words: chaotic system, Routh--Hurwitz criterion, Hopf bifurcation, feedback control

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

  • 05.45.Gg
05.45.Pq (Numerical simulations of chaotic systems) 07.05.Dz (Control systems)