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

被引：0
|
作者：
Wu Zheng-Mao [1 ]
Lu Jun-Guo [1 ]
Xie Jian-Ying [1 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Automat, Shanghai 200030, Peoples R China
来源：
CHINESE PHYSICS | 2006年 / 15卷 / 06期
关键词：
fractional-order system; harmonic balance principle; Genesio-Tesi system; chaos; Lur'e system;
D O I：
暂无
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
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.
引用
收藏
页码：1201 / 1207
页数：7
相关论文
共 50 条
  • [1] Analysing chaos in fractional-order systems with the harmonic balance method
    Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China
    Chin. Phys., 2006, 6 (1201-1207):
  • [2] AN EFFECTIVE METHOD FOR DETECTING CHAOS IN FRACTIONAL-ORDER SYSTEMS
    Cafagna, Donato
    Grassi, Giuseppe
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2010, 20 (03): : 669 - 678
  • [3] CHAOS AND ADAPTIVE SYNCHRONIZATIONS IN FRACTIONAL-ORDER SYSTEMS
    Liu, Xiaojun
    Hong, Ling
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (11):
  • [4] Chaos synchronization of fractional-order differential systems
    Li, CP
    Deng, WH
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2006, 20 (07): : 791 - 803
  • [5] Impulsive stabilization of chaos in fractional-order systems
    Marius-F. Danca
    Michal Fečkan
    Guanrong Chen
    Nonlinear Dynamics, 2017, 89 : 1889 - 1903
  • [6] Impulsive stabilization of chaos in fractional-order systems
    Danca, Marius-F.
    Feckan, Michal
    Chen, Guanrong
    NONLINEAR DYNAMICS, 2017, 89 (03) : 1889 - 1903
  • [7] Chaos in fractional-order autonomous nonlinear systems
    Ahmad, WM
    Sprott, JC
    CHAOS SOLITONS & FRACTALS, 2003, 16 (02) : 339 - 351
  • [8] Dynamical analysis of fractional-order nonlinear oscillator by incremental harmonic balance method
    Shen, Yong-Jun
    Wen, Shao-Fang
    Li, Xiang-Hong
    Yang, Shao-Pu
    Xing, Hai-Jun
    NONLINEAR DYNAMICS, 2016, 85 (03) : 1457 - 1467
  • [9] Harmonic Balance Method for Chaotic Dynamics in Fractional-Order Rossler Toroidal System
    Zhu, Huijian
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2013, 2013
  • [10] Dynamical analysis of fractional-order nonlinear oscillator by incremental harmonic balance method
    Yong-Jun Shen
    Shao-Fang Wen
    Xiang-Hong Li
    Shao-Pu Yang
    Hai-Jun Xing
    Nonlinear Dynamics, 2016, 85 : 1457 - 1467
12345