中国物理B ›› 2007, Vol. 16 ›› Issue (8): 2264-2271.doi: 10.1088/1009-1963/16/8/018

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Continuous feedback control of KdV Burgers system

薛具奎1, 张丽萍2   

  1. (1)College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China; (2)School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China
  • 收稿日期:2006-09-12 修回日期:2006-12-18 出版日期:2007-08-20 发布日期:2007-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10475066 and 10347006).

Continuous feedback control of KdV Burgers system

Zhang Li-Ping(张丽萍)a)† and Xue Ju-Kui(薛具奎)b)   

  1. a School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China; b College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
  • Received:2006-09-12 Revised:2006-12-18 Online:2007-08-20 Published:2007-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10475066 and 10347006).

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摘要： The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationary points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment separately.

关键词: KdV Burgers equation, chaos attractor, stationary points, periodic orbit

Abstract: The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationary points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment separately.

Key words: KdV Burgers equation, chaos attractor, stationary points, periodic orbit

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

  • 05.45.Gg
02.30.Jr (Partial differential equations) 05.45.Pq (Numerical simulations of chaotic systems)