中国物理B ›› 2006, Vol. 15 ›› Issue (6): 1201-1207.doi: 10.1088/1009-1963/15/6/013

• GENERAL • 上一篇    下一篇

Analysing chaos in fractional-order systems with the harmonic balance method

吴峥茂, 卢俊国, 谢剑英   

  1. Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China
  • 收稿日期:2005-09-29 修回日期:2006-03-23 出版日期:2006-06-20 发布日期:2006-06-20

Analysing chaos in fractional-order systems with the harmonic balance method

Wu Zheng-Mao (吴峥茂), Lu Jun-Guo (卢俊国), Xie Jian-Ying (谢剑英)   

  1. Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China
  • Received:2005-09-29 Revised:2006-03-23 Online:2006-06-20 Published:2006-06-20

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摘要： In this paper, the fractional-order Genesio--Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.

Abstract: In this paper, the fractional-order Genesio--Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.

Key words: fractional-order system, harmonic balance principle, Genesio--Tesi system, chaos, Lur'e system

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

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