Journal of South China University of Technology (Natural Science Edition) ›› 2008, Vol. 36 ›› Issue (8): 6-10.

• Electronics, Communication & Automation Technology • Previous Articles     Next Articles

Chaotic Dynamic Characteristics of Fractional-Order Unified System

Sun Ke-hui1  Ren Jian2  Qiu Shui-sheng1   

  1. 1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, Guangdong, China; 2. School of Physics Science and Technology, Central South University, Changsha 410083, Hunan, China
  • Received:2007-08-30 Revised:2007-11-13 Online:2008-08-25 Published:2008-08-25
  • Contact: 孙克辉（1968-），男，在站博士后，主要从事混沌理论及其应用研究． E-mail:kehui_csu@hotmail．com
  • About author:孙克辉（1968-），男，在站博士后，主要从事混沌理论及其应用研究．
  • Supported by:

    国家自然科学基金资助项目（60672041）;中国博士后基金项目（20070420774）

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Abstract:

In order to investigate the chaos generally existing in nonlinear fractional-order systems, the dynamic characteristics of the fractional-order unified system varying with the differential operator orders respectively with fixed （ a = 1 ） and variable parameter are analyzed by observing the phase diagrams of system attractors and by calculating the power spectral density and the maximum Lyapunov exponent. The rules of chaos occurrence in the fractional-order unified system varying with the system parameter and the fractional order are then obtained, Moreover, the routs to chaos in the fractional order unified system are studied. The results show that （ 1 ） the dynamic states of the fractional-order unified system are related to both the system parameter and the fractional order; （2） the fractional-order unified systems with fixed and variable parameter are all piecewise chaotic at different fractional orders ; and （3） with the variation of system parameter at a differential operator order of 0.3, the fractional-order unified system enters into chaotic state by transient chaos and boundary crisis bifurcation. It is thus concluded that the fractional-order unified system is of complex dynamic characteristics.

Key words: fractional-order system, unified chaotic system, chaos, dynamic characteristic