中国物理B ›› 2009, Vol. 18 ›› Issue (12): 5235-5241.doi: 10.1088/1674-1056/18/12/021

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Bifurcation control and chaos in a linear impulsive system

胥布工1, 杨启贵2, 蒋贵荣3   

  1. (1)College of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China; (2)School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China; (3)School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China \addressb)School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
  • 收稿日期:2008-11-07 修回日期:2009-06-26 出版日期:2009-12-20 发布日期:2009-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10871074 and 10572011) and the Natural Science Foundation of Guangxi Province, China (Grant No 0832244).

Bifurcation control and chaos in a linear impulsive system

Jiang Gui-Rong(蒋贵荣)a)b),Xu Bu-Gong(胥布工) c), and Yang Qi-Gui (杨启贵)a)†   

  1. a School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China; b School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China; c College of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China
  • Received:2008-11-07 Revised:2009-06-26 Online:2009-12-20 Published:2009-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10871074 and 10572011) and the Natural Science Foundation of Guangxi Province, China (Grant No 0832244).

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摘要： Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.

Abstract: Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.

Key words: periodic solution, bifurcation control, chaos, controller

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

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