TY - JOUR
T1 - Dynamic analysis of a fractional-order Lorenz chaotic system
AU - Yu, Yongguang
AU - Li, Han-Xiong
AU - Wang, Sha
AU - Yu, Junzhi
PY - 2009/10/30
Y1 - 2009/10/30
N2 - 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. © 2009 Elsevier Ltd. All rights reserved.
AB - 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. © 2009 Elsevier Ltd. All rights reserved.
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U2 - 10.1016/j.chaos.2009.03.016
DO - 10.1016/j.chaos.2009.03.016
M3 - RGC 21 - Publication in refereed journal
SN - 0960-0779
VL - 42
SP - 1181
EP - 1189
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 2
ER -