| GENERAL |
|
|
|
|
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 |
|
| Cite this article: |
|
YANG Yun-Qing, CHEN Yong 2009 Chin. Phys. Lett. 26 100501 |
|
|
|
|
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.
|
| Keywords:
05.45.-a
05.45.Xt
|
|
|
Received: 06 May 2009
Published: 27 September 2009
|
|
| PACS: |
05.45.-a
|
(Nonlinear dynamics and chaos)
|
| |
05.45.Xt
|
(Synchronization; coupled oscillators)
|
|
|
|
|
|
[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 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
