Complex dynamical behavior and chaos control in fractional-order Lorenz-like systems

Chinese Physics B

Volumn 22, Issue 4, 2013, Pages

  Li, Rui Hong ^a   Chen, Wei Sheng ^a  

^a XIDIAN UNIVERSITY   (China)

Author keywords

chaos control; fractional order Lorenz like system; pitchfork bifurcation; stability analysis

Indexed keywords

CHAOS CONTROL; EXISTENCE AND UNIQUENESS OF SOLUTION; FRACTIONAL-ORDER SYSTEMS; LARGEST LYAPUNOV EXPONENT; LORENZ-LIKE SYSTEMS; PITCH-FORK BIFURCATIONS; STABILITY ANALYSIS; UNSTABLE EQUILIBRIUM POINTS;

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; LYAPUNOV METHODS;

DYNAMICS;

EID: 84876134849     PISSN: 16741056     EISSN: None     Source Type: Journal    
DOI: 10.1088/1674-1056/22/4/040503     Document Type: Article

References (36)

1. Oldham K B and Spanier J 1974 The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order (New York: Academic Press)
2. Miller K S and Ross B 1993 An Introduction to the Fractional Calculus and Fractional Differential Equations (New York: John Wiley and Sons)
3. Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
4. Sheu L J, Chen H K, Chen J H, Tam L M, Chen W C, Lin K T and Kang Y 2008 Chaos, Solitons Fractals 36 98 (Pubitemid 47576640)
5. Engheta N 1996 IEEE Trans. Anten. Propag. 44 554
6. Bagley R L and Calico R A 1991 J. Guid. Control Dyn. 14 304
7. Ahmad W M and Ei-Khazali R 2007 Chaos, Solitons Fractals 33 1367 (Pubitemid 46413017)
8. El-Sayed A M A 1996 Int. J. Theor. Phys. 35 311
9. Lazopoulos K A 2006 Mech. Res. Commun. 33 753 (Pubitemid 44037770)
10. Laskin N 2000 Physica A 287 482 (Pubitemid 32034792)
11. Chen J H and Chen W C 2008 Chaos, Solitons Fractals 35 188 (Pubitemid 47385209)
12. Shao S Q, Gao X and Liu X W 2007 Chin. Phys. 16 2612
13. Zhou P, Wei L J and Cheng X F 2009 Chin. Phys. B 18 2674
14. Xu Z, Liu C X and Yang T 2010 Acta Phys. Sin. 59 1524 (in Chinese)
15. Zhang R X, Yang S P and Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese)
16. Yan X M and Liu D 2010 Acta Phys. Sin. 59 3043 (in Chinese)
17. Yang J and Qi D L 2010 Chin. Phys. B 19 020508
18. Niu Y J, Wang X Y, Nian F Z and Wang M J 2010 Chin. Phys. B 19 120507
19. Schuster H G 1984 Deterministic Chaos: An Introduction (Weinheim: Physik-Verlag)
20. Liu C X, Liu L, Liu T and Li P 2006 Chaos, Solitons Fractals 28 1196 (Pubitemid 41815091)
21. Deng W H 2010 Nonlinear Analysis: Theor., Methods Appl. 72 1768
22. Deng W H, Li C P and Guo Q 2007 Fractals 15 173 (Pubitemid 46970248)
23. Diethelm K and Ford N J 2002 J. Math. Anal. Appl. 265 229
24. Diethelm K and Freed A D 1999 On the Solution of Nonlinear Fractional-order Differential Equations Used in the Modeling of Viscoplasticity (Heidelberg: Springer-Verlag)
25. Diethelm K, Ford N J and Freed A D 2009 Nonlinear Dyn. 29 3
26. El-Mesiry A E M, El-Sayed A M A and El-Saka H A A 2005 Appl. Math. Comput. 160 683
27. Deng W H 2007 J. Comput. Phys. 227 1510
28. Qian D L 2010 "Stability Analysis and Normal Form Computation of Fractional Differential Equations" PhD Dissertation (Shanghai: Shanghai University)
29. Rosenstein M T, Collins J J and De Luca C J 1993 Physcia D 65 117
30. Park J H 2005 Chaos, Solitons Fractals 23 1049
31. Lee T H and Park J H 2009 Chin. Phys. Lett. 26 090507
32. Lee S M, Kwon O M and Park J H 2011 Chin. Phys. B 20 010506
33. Ji D H, Koo J H, Won S C and Park J H 2011 Chin. Phys. B 20 070502
34. Dadras S and Momeni H R 2010 Physica A 389 2434
35. Qi D L, Yang J and Zhang J L 2010 Chin. Phys. B 19 100506
36. Chen D Y, Liu Y X, Ma X Y and Zhang R F 2012 Nonlinear Dyn. 67 893