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Dynamic analysis of a fractional-order Lorenz chaotic system

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  • Yu, Yongguang
  • Li, Han-Xiong
  • Wang, Sha
  • Yu, Junzhi

Abstract

The dynamic behaviors of fractional-order differential systems have received increasing attention in recent decades. But many results about fractional-order chaotic systems are attained only by using analytic and numerical methods. Based on the qualitative theory, the existence and uniqueness of solutions for a class of fractional-order Lorenz chaotic systems are investigated theoretically in this paper. The stability of the corresponding equilibria is also argued similarly to the integer-order counterpart. According to the obtained results, the bifurcation conditions of these two systems are significantly different. Numerical solutions, together with simulations, finally verify the correctness of our analysis.

Suggested Citation

  • Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1181-1189
    DOI: 10.1016/j.chaos.2009.03.016
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