中国物理B ›› 2008, Vol. 17 ›› Issue (7): 2405-2411.doi: 10.1088/1674-1056/17/7/013

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Controlling bifurcations and chaos in discrete small-world networks

关治洪1, 王华2, 刘峰3   

  1. (1)Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; (2)Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;Department of Aerospace Mechanical Engineering, Boston University, Boston, MA 02215, USA; (3)School of Electronic Information and Mechanics, China University of Geosciences, Wuhan 430074, China;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:2006-11-07 修回日期:2007-11-16 出版日期:2008-07-09 发布日期:2008-07-09
  • 基金资助:
    Project supported by the Research Foundation for Outstanding Young Teachers of China University of Geosciences, China (Grant No CUGNL0637) and the National Natural Science Foundation of China (Grant Nos 60573005, 60603006 and 60628301).

Controlling bifurcations and chaos in discrete small-world networks

Liu Feng(刘峰)a)b) † , Guan Zhi-Hong(关治洪)b), and Wang Hua(王华)b)c)   

  1. a School of Electronic Information and Mechanics, China University of Geosciences, Wuhan 430074, China; b Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; c Department of Aerospace Mechanical Engineering, Boston University, Boston, MA 02215, USA
  • Received:2006-11-07 Revised:2007-11-16 Online:2008-07-09 Published:2008-07-09
  • Supported by:
    Project supported by the Research Foundation for Outstanding Young Teachers of China University of Geosciences, China (Grant No CUGNL0637) and the National Natural Science Foundation of China (Grant Nos 60573005, 60603006 and 60628301).

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摘要： We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that the bifurcations can be delayed or completely eliminated. A periodic orbit of the system can be controlled to any desired periodic orbit by using this method.

关键词: bifurcation, chaos, small-world networks, impulsive hybrid control

Abstract: We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that the bifurcations can be delayed or completely eliminated. A periodic orbit of the system can be controlled to any desired periodic orbit by using this method.

Key words: bifurcation, chaos, small-world networks, impulsive hybrid control

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

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