Synchronization of fractional hyperchaotic Lü system via unidirectional coupling method

Proceedings of the World Congress on Intelligent Control and Automation (WCICA)

Volumn , Issue , 2008, Pages 4653-4658

  Liu, Jie ^a   Li, Xinjie ^a  

^a WUHAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; SYNCHRONIZATION;

FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER HYPERCHAOTIC; FRACTIONAL-ORDER SYSTEMS; NUMERICAL ALGORITHMS; NUMERICAL EXPERIMENTS; SYNCHRONIZATION PROBLEM; SYNCHRONIZATION SCHEME; UNIDIRECTIONAL COUPLING;

NUMERICAL METHODS;

EID: 52149114683     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/WCICA.2008.4593675     Document Type: Conference Paper

References (31)

1. Podlubny I. Fractional differential equations. New York: Academic Press; 1999.
2. Hilfer R, editor. Applications of fractional calculus in physics. New Jersey: World Scientific; 2001.
3. Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calc Appl Anal 2002; 5(4): 367-86.
4. A M Chen, J-A Lu., J H Lü., and X M Yu., Generating hyperchaotic Lü attractor via stste feedback control. Physica A. 2006; 64: 103-110.
5. El-Sayed AMA, El-Mesiry AEM, El-Saka HAA. Numerical solution for multi-term fractional (arbitrary) orders differential equations. Comput Appl Math 2004; 23: 33C54.
6. Diethelm K, Ford NJ. Multi-order fractional differential equations and their numerical solution. Appl Math Comput 2004; 154: 621C40.
7. Leszczynski J, Ciesielski M. A numerical method for solution of ordinary differential equations of fractional order, math.NA/ 0202276 V1 26 Feb 2002.
8. Diethelm K, Ford NJ, Freed AD. A predictorCcorrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 2002; 29: 3C22.
9. Wolf A., Swinney J. B., Swinney H L., Vastano JA. Determining Lyapunov exponents from a time series. Phys D 1985,16: 285C317.
10. Hartley TT, Lorenzo CF, Qammer HK. Chaos in a fractional order Chua's system. IEEE Trans CAS-I 1995,42: 485-490.
11. Sun HH, Abdelwahad AA, Onaral B. Linear approximation of transfer function with a pole of fractional order. IEEE Trans Automat Contr 1984,29: 441-4.
12. Charef A, Sun HH, Tsao YY, Onaral B. Fractal system as represented by singularity function. IEEE Trans Automat Contr 1992, 37: 1465-1470.
13. A. Oustaloup, F. Levron, F. Nanot and B. Mathieu, Frequency band complex non integer differentiator: characterization and synthesis. IEEE Trans. CAS-I, 2000, 47: 25C40.
14. Y.Q. Chen and K. Moore, Discretization schemes for fractional-order differentiators and integrators. IEEE Trans. CAS-I 49 (2002):363C367.
15. Long Jye Sheu., Hsien Keng Chen., Juhn Horng Chen., and Lap Mou Tam., Chaotic dynamics in fractionally damped Duffing equation, Chaos, Solitons & Fractals, doi: 10.1016/j.chaos. 2005.11.066, 2005.
16. Gao X., Yu J., Chaos in the fractional order periodically forced complex Duffings equation. Chaos, Solitons & Fractals. 2005; 24: 1097-04.
17. Li C. P., Peng G. J., Chaos in Chen's system with a fractional order. Chaos, Solitons & Fractals 2004, 22: 443-50.
18. Li C. G., Chen G. Chaos and hyperchaos in fractional order Rössler equations. Physica A, 2004,341: 55-61.
19. Li C. G., Chen G. Chaos in the fractional order Chen system and its control. Chaos, Solitons and Fractals 2004;22:549-54.
20. J. G. Lu. Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos, Solitions, and Fractals, 2005, 26(4):1125-1133.
21. J. G. Lu and G Chen. A note on the fractional-order Chen system. Chaos, Solitions, and Fractals, 2006, 27(3):685-688.
22. J. G. Lu., Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal. Physica A. 2006, 359:107-118.
23. J. W. Wang, X Xiong, Y Zhang., Extending synchronization scheme to chaotic fractional-order Chen systems. Physica A 2006, 370: 279-285.
24. J. W. Wang., Y Zhang., Designing synchronization schemes for chaotic fractional-order unified systems. Chaos, Solitons and Fractals. 2006, 30:1265-1272.
25. Wu Zheng-mao et al., Synchronization in a unified fractional-order chaotic system. Chinese Phys. 2007,16:1901-1907.
26. W. H. Deng and J. Lü. Design of multi-directional multi-scroll chaotic attractors based on fractional differential systems via switching control. Chaos, 2006, 16(4): 43120.
27. W. H. Deng, C. P. Li and J. Lü. Stability analysis of linear fractional differential system with multiple time-delays. Nonlinear Dynamics, 2007, 48(4): 409-416.
28. Ahmad W. M., Sprott J. C., Chaos in fractional-order autonomous nonlinear systems. Chaos, Solitons and Fractals 2003, 16:339-51.
29. Ahmad W. M., Harb A., On nonlinear control design for autonomous chaotic systems of integer and fractional orders. Chaos, Solitons and Fractals 2003, 18:693-701.
30. El-Khazali R., Ahmad W. M., Al-Assaf Y., Sliding mode control of fractional chaotic systems. In: Proceedings of IFAC workshop on Fractional Differentiation and its Application, France, 2004, July:495-500.
31. Ahmad W. M., El-Khazali R., Al-Assaf Y., Stabilization of fractional chaotic systems using state-feedback control. Chaos, Solitons and Fractals 2004, 22.1:141-50.