中国物理B ›› 2008, Vol. 17 ›› Issue (5): 1691-1697.doi: 10.1088/1674-1056/17/5/026

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Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

唐驾时1, 秦金旗1, 刘素华2, 尹小波3   

  1. (1)College of Mechanics and Aerospace, Hunan University, Changsha 410082, China; (2)College of Mechanics and Aerospace, Hunan University, Changsha 410082, China;Anyang Institute of Technology, Anyang 455000, China; (3)School of Geoscience and Environmental Engineering, Central South University, Changsha 410083, China
  • 收稿日期:2007-07-26 修回日期:2007-11-29 出版日期:2008-05-20 发布日期:2008-05-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10672053).

Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

Liu Su-Hua(刘素华)a)b)† , Tang Jia-Shi(唐驾时)a), Qin Jin-Qi(秦金旗)a), and Yin Xiao-Bo(尹小波)c)   

  1. a College of Mechanics and Aerospace, Hunan University, Changsha 410082, China; b Anyang Institute of Technology, Anyang 455000, China; c School of Geoscience and Environmental Engineering, Central South University, Changsha 410083, China
  • Received:2007-07-26 Revised:2007-11-29 Online:2008-05-20 Published:2008-05-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10672053).

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摘要： Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.

关键词: Langford system, nonlinear control, secondary Hopf bifurcation, torus

Abstract: Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.

Key words: Langford system, nonlinear control, secondary Hopf bifurcation, torus

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

  • 05.45.Gg
02.30.Oz (Bifurcation theory)