Chaos in the Fractional Order Generalized Lorenz Canonical Form
YANG Yun-Qing1, CHEN Yong1,2
1Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 2000622Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211
Chaos in the Fractional Order Generalized Lorenz Canonical Form
YANG Yun-Qing1, CHEN Yong1,2
1Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 2000622Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211
摘要A fractional-order generalized Lorenz system is constructed and numerically investigated. Chaotic behavior existing in the fractional-order generalized Lorenz system is found. The numerical simulations and interesting figures are performed.
Abstract：A fractional-order generalized Lorenz system is constructed and numerically investigated. Chaotic behavior existing in the fractional-order generalized Lorenz system is found. The numerical simulations and interesting figures are performed.
YANG Yun-Qing; CHEN Yong;. Chaos in the Fractional Order Generalized Lorenz Canonical Form[J]. 中国物理快报, 2009, 26(10): 100501-100501.
YANG Yun-Qing, CHEN Yong,. Chaos in the Fractional Order Generalized Lorenz Canonical Form. Chin. Phys. Lett., 2009, 26(10): 100501-100501.
[1] Leibniz G W 1962 Mathematische Schriften 1849(Berlin: Olms Verlag Hildesheim) 2 301 [2]Sabatier J, Agrawal O P and Tenreiro Machado J A 2007 Advances in Fractional Calculus: Theoretical Developments andApplications in Physics and Engineering (Netherlands: Springer) [3]Samko S G, Klibas A A and Marichev O I 1993 FractionalIntegrals and Derivatives: Theory and Applications (New York:Gordon and Breach Science Publishers) [4]Diethelm K, Ford N J and Freed A D 2002 Nonlin. Dyn. 29 3 [5]Chen Y and Yan Z 2003 Appl. Math. Mech. 24 256 [6]Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 034101 [7]Hartley T T, Lorenzo C F and Qammer H K 1995 IEEETrans Circuits and Systems I 42 485 [8]Yu Y, Li H X, Wang S and Yu J 2009 Chaos Solitons andFractals 22 1181 [9]Deng W H and Li C P 2005 Physica A 353 61 [10]Li C and Peng J 2004 Chaos Solitons and Fractals 22 443 [11]Wang X Y and Wang M J 2007 Chaos 17 033106 [12]Celikovsky S and Chen G 2002 Int. J. Bifurcation andChaos 12 1789 [13]Celikovsky S and Chen G 2005 Chaos Solitons andFractals 26 1271 [14]Shimizu T and Morioka N 1976 Phys. Lett. A 76201 [15]L\"{u Z S and Duan L X 2009 Chin. Phys. Lett. 26 050504 [16]Lorenz E N 1963 Atmos J Sci 20 130 [17]Liu L, Liu C X and Zhang Y B 2007 Chin. Phys. Lett. 24 2756 [18]Mossa Al-Sawalha and Noorani M S M 2008 Chin. Phys.Lett. 25 1217 [19]L\"{u J and Chen G 2002 Int. J. Bifurcation andChaos 12 2917 [20]Bao B C and Liu Z 2008 Chin. Phys. Lett. 252396 [21]Chen G and Ueta T 1999 Int. J. Bifurcation and Chaos 9 1465 [22]Yang Y and Chen Y 2009 Chaos, Solitons and Fractals 39 2378 [23]Yan Z 2005 Chaos 15 023902
2009, Vol. 26 
