Dynamic analysis of the fractional-order Liu system and its synchronization.

Based on the stability theory of fractional-order systems, the dynamic behaviors of fractional-order Liu system are studied theoretically. Coupling synchronization of two identical fractional-order chaotic systems is also studied and a simple criterion is presented. Numerical simulations show the effectiveness of our methods.

[1]  G. Benettin,et al.  Kolmogorov Entropy and Numerical Experiments , 1976 .

[2]  P. Arena,et al.  Nonlinear Noninteger Order Circuits and Systems — An Introduction , 2000 .

[3]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

[4]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.

[5]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[6]  Heidelberg,et al.  Observation of a chiral state in a microwave cavity. , 2002, Physical review letters.

[7]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[8]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[9]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[10]  Faqiang Wang,et al.  A new criterion for chaos and hyperchaos synchronization using linear feedback control , 2006 .

[11]  Changpin Li,et al.  Chaos in Chen's system with a fractional order , 2004 .

[12]  Juebang Yu,et al.  Chaos in the fractional order periodically forced complex Duffing’s oscillators , 2005 .

[13]  R. Koeller.  Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics , 1986 .

[14]  R. Koeller.  Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .

[15]  W. Deng,et al.  Chaos synchronization of the fractional Lü system , 2005 .

[16]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[17]  R. Bagley,et al.  Fractional order state equations for the control of viscoelasticallydamped structures , 1991 .

[18]  I. Podlubny.  Fractional differential equations , 1998 .