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.
Received: 29 September 2005
Revised: 23 March 2006
Accepted manuscript online:
Wu Zheng-Mao (吴峥茂), Lu Jun-Guo (卢俊国), Xie Jian-Ying (谢剑英) Analysing chaos in fractional-order systems with the harmonic balance method 2006 Chinese Physics 15 1201
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