Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 8, 2009, Pages 3351-3357

  Wang, Xing Yuan ^a   Song, Jun Mei ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Activation feedback control; Chaotic synchronization; Fractional order hyperchaos Lorenz system

Indexed keywords

CHAOTIC SYSTEMS; CHEMICAL ACTIVATION; NUMERICAL METHODS; SYNCHRONIZATION;

ACTIVATION FEEDBACK CONTROL; CHAOTIC SYNCHRONIZATION; FRACTIONAL ORDER; FRACTIONAL ORDER HYPERCHAOS LORENZ SYSTEM; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; HYPERCHAOS; LORENZ SYSTEM; PAPER ANALYSIS; STABILITY THEORIES;

FEEDBACK CONTROL;

EID: 60849138778     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.01.010     Document Type: Article

References (23)

1. Podlubny I. Fractional differential equations (1999), Academic Press, New York
2. Hilfer R. Applications of fractional calculus in physics (2001), World Scientific, New Jersey
3. Bagley R.L., and Calico R.A. Fractional order state equations for the control of viscoelastically damped structures. J Guidance Control Dyn 14 2 (1991) 304-311
4. Koeller R.C. Application of fractional calculus to the theory of viscoelasticity. J Appl Mech 51 2 (1984) 294-298
5. Koeller R.C. Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics. Acta Mech 58 3-4 (1986) 251-264
6. Heaviside O. Electromagnetic theory (1971), Chelsea, New York
7. Grigorenko I., and Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 91 3 (2003) 034101
8. Hartley T.T., Lorenzo C.F., and Qammer H.K. Chaos in a fractional order Chua's system. IEEE Trans CAS-I 42 8 (1995) 485-490
9. Li C.G., and Chen G.R. Chaos in the fractional order Chen system and its control. Chaos Solitons Fract 22 3 (2004) 549-554
10. Li C.P., and Peng G.J. Chaos in Chen's system with a fractional order. Chaos Solitons Fract 22 2 (2004) 443-450
11. Li C.P., and Deng W.H. Chaos synchronization of fractional-order differential system. Int J Mod Phys B 20 7 (2006) 791-803
12. Tavazoei M.S., and Haeri M. Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems. IET Signal Processing 1 4 (2007) 171-181
13. Deng W.H., and Li C.P. Chaos synchronization of the fractional Lü system. Physica A 353 (2005) 61-72
14. Wang X.Y., and Song J.M. Synchronization of the unified chaotic system. Nonlinear Anal: Theory Meth Appl 69 10 (2008) 3409-3416
15. Caputo M. Linear models of dissipation whose Q is almost frequency independent. Geophys J Roy Astronom Soc 13 (1967) 529-539
16. Matignon D. Stability results for fractional differential equations with application to control processing. Computational engineering system application vol. 2 (1996), IMACS-SMC, Lille (France) 963-968
17. Mohammad S.T., and Mohammad H. A note on the stability of fractional order systems. Math Comput Simulat (2007) 10.1016/j.matcom.2008.07.003
18. Lorenz E.N. Deterministic nonperodic flow. J Atmos Sci 20 (1963) 130-141
19. Wang X.Y., and Wang M.J. A hyperchaos generated from Lorenz system. Physica A 387 14 (2008) 3751-3758
20. Petras I. A note on the fractional-order Chua's system. Chaos Solitons Fract 38 1 (2008) 140-147
21. Ramasubramanian K., and Sriram M.S. A comparative study of computation of Lyapunov spectra with different algorithms. Physica D 139 1, 2 (2000) 72-86
22. Wang Y.H., and Li C.P. Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?. Phys Lett A 363 5&6 (2007) 414-419
23. Li C.P., and Deng W.H. Synchronization of limit sets. Mod Phys Lett B 21 9 (2007) 551-558