Control and switching synchronization of fractional order chaotic systems using active control technique

Journal of Advanced Research

Volumn 5, Issue 1, 2014, Pages 125-132

  Radwan, A G ^a   Moaddy, K ^b   Salama, K N ^c   Momani, S ^d   Hashim, I ^b  

^a CAIRO UNIVERSITY   (Egypt)

^b UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

^c KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

^d UNIVERSITY OF JORDAN   (Jordan)

Author keywords

Chaotic systems; Control; Fractional calculus; Fractional order synchronization; Non standard finite difference schemes; Switching control

Indexed keywords

EID: 84892575233     PISSN: 20901232     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jare.2013.01.003     Document Type: Article

References (38)

1. Baleanu D., Diethelm K., Scalas E., Trujillo J. Fractional calculus models and numerical methods 2009, World Scientific, Singapore.
2. Heymans N., Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheological Acta 2005, 45:765-771.
3. Radwan A.G., Moaddy K., Momani S. Stability and nonstandard finite difference method of the generalized Chua's circuit. Comput Math Appl 2011, 62:961-970.
4. Radwan A.G., Shamim A., Salama K.N. Theory of fractional-order elements based impedance matching networks. IEEE Microw Wireless Compon Lett 2011, 21(3):120-122.
5. Kaczorek T. Practical stability and asymptotic stability of positive fractional 2D linear systems. Asian J Control 2010, 12(2):200-207.
6. Li Y., Chen Y.Q., Ahn H.S. Fractional order iterative learning control for fractional order linear systems. Asian J Control 2011, 13(1):54-63.
7. Li C.P., Deng W.H. Remarks on fractional derivatives. Appl Math Comput 2007, 187:777-784.
8. Podlubny Fractional differential equations 1999, Academic Press, New York.
9. Magin R.L. Fractional calculus models of complex dynamics in biological tissues. Comput Math Appl 2010, 59:1586-1593.
10. Radwan A.G., Elwakil A.S., Soliman A.S. Fractional-order sinusoidal oscillators: design procedure and practical examples. IEEE Trans Circ Syst I 2008, 55:2051-2063.
11. Radwan A.G., Soliman A.M., Elwakil A.S. First-order filters generalized to the fractional domain. J Circ Syst Comp 2008, 17:55-66.
12. α circuit. IEEE Trans Circ Syst I 2011, 58(10):2388-2397.
13. Radwan A.G., Soliman A.M., EL-sedeek A.L. An inductorless CMOS realization of Chua's circuit. Chaos, Solitons Fractals 2004, 18:149-158.
14. Radwan A.G., Soliman A.M., EL-sedeek A.L. MOS realization of the modified Lorenz chaotic system. Chaos, Solitons Fractals 2004, (21):553-561.
15. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys Rev Lett 1990, 64:821-824.
16. Moaddy K., Radwan A.G., Salama K.N., Momani S., Hashim I. The fractional-order modeling and synchronization of electrically coupled neurons system. Comput Math Appl 2012, 64:3329-3339.
17. Park J.H., Kwon O.M. A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos Soliton Fract 2005, 23:495-501.
18. Chen S.H., Lu J. Synchronization of an uncertain unified chaotic system via adaptive control. Chaos Soliton Fract 2002, 14:643-647.
19. Ho M.C., Hung Y.C. Synchronization of two different systems by using generalized active control. Phys Lett A 2002, 301:424-429.
20. Vincent U.E. Chaos synchronization using active control and backstepping control: a comparative analysis. Nonlin Anal Model Control 2008, 13:253-261.
21. Li C.P., Yan J.P. The synchronization of three fractional differential systems. Chaos Soliton Fract 2007, 32:751-757.
22. Yu Y., Li H.X., Su Y. The synchronization of three chaotic fractional-order Lorenz systems with bidirectional coupling. J Phys: Conf Ser 2008, 96(1):112-113.
23. Odibata Z.M., Corsonb N., Aziz-Alaouib M.A., Bertellec C. Synchronization of chaotic fractional-order systems via linear control. Int J Bifurcat Chaos 2010, 20(1):1-15.
24. Bhalekar S., Daftardar-Gejji V. Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simulat 2010, 15:3536-3546.
25. Yua Y., Lib H.X. The synchronization of fractional-order Rössler hyperchaotic systems. Phys A 2008, 387:1393-1403.
26. Yan J., Li C. On chaos synchronization of fractional differential equations. Chaos, Solitons Fractals 2007, 32(2):725-735.
27. Aboelela M.A.S., Ahmed M.F., Dorrah H.T. Design of aerospace control systems using fractional PID controller. J Adv Res 2012, 3:225-232.
28. Kusyk J., Sahin C.S., Uyar M.U., Urrea E., Gundry S. Self-organization of nodes in mobile ad hoc networks using evolutionary games and genetic algorithms. J Adv Res 2011, 2:253-264.
29. Radwan A.G. On some generalized discrete logistic maps. J Adv Res 2013, 4(2):163-171.
30. Mickens R.E. Nonstandard finite difference models of differential equations 1994, World Scientific, Singapore.
31. Mickens R.E. Advances in the Applications of Nonstandard Finite Difference Schemes 2005, World Scientific, Singapore.
32. Kaslik E., Sivasundaram S. Analytical and numerical methods for the stability analysis of linear fractional delay differential equations. J Comput Appl Math 2012, 236(16):4027-4041.
33. Demirci E., Ozalp N. A method for solving differential equations of fractional order. J Comput Appl Math 2012, 236(11):2754-2762.
34. Hussian G, Alnaser M, Momani S. Non-standard discretization of fractional differential equations. In: Proc 8th seminar of diff equ Dyn Syst, Isfahan, Iran; 2008.
35. Lü J.G. Chaotic dynamics of the fractional order Lü system and its synchronization. Phys Lett A 2006, 354(4):305-311.
36. Perc M. User friendly programs for nonlinear time series analysis. [Retrieved 07.08.10]. http://www.matjazperc.com/ejp/time.html.
37. Kang Y., Lin K.T., Chen J.H., Sheu L.J., Chen H.K. Parametric analysis of a fractional-order Newton-Leipnik system. J Phys: Conf Ser 2008, 96:012140.
38. Radwan A.G., Soliman A.M., Elwakil A.S., Sedeek A. On the stability of linear systems with fractional order elements. Chaos, Solitons Fractals 2009, 40(5):2317-2328.