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SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL

Faculty of Science and Technology, University of Le Havre, 76058 Le Havre Cedex, France

On sabbatical leave from Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt-Jordan.

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NATHALIE CORSON

Appl. Math. Lab., University of Le Havre, 76058, Le Havre Cedex, France

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M. A. AZIZ-ALAOUI

Appl. Math. Lab., University of Le Havre, 76058, Le Havre Cedex, France

Author for correspondence.

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, and

CYRILLE BERTELLE

LITIS, University of Le Havre, 76058 Le Havre Cedex, France

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https://doi.org/10.1142/S0218127410025429Cited by:102

Abstract

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rössler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis.

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References

A. Arneodoet al., Physica D 14, 327 (1985), DOI: 10.1016/0167-2789(85)90093-4. Crossref, ISI, Google Scholar
M. A. Aziz-Alaoui, Encyclopedia of Mathematical Physics (Elsevier, 2006) pp. 213–226. Crossref, Google Scholar
M. Caputo, J. Roy. Astr. Soc. 13, 529 (1967). Crossref, ISI, Google Scholar
C. Chen and T. Ueta, Int. J. Bifurcation and Chaos 9, 1465 (1999). Link, ISI, Google Scholar
G. Chen and X. Dong , From Chaos to Order: Methodologies, Persectives and Applications ( World Scientific , Singapore , 1998 ) . Crossref, Google Scholar
L. O. Chua and G.-N. Lin, IEEE Trans. Circuits Syst. 37, 885 (1990), DOI: 10.1109/31.55064. Crossref, Google Scholar
L. O. Chuaet al., J. Circuits Syst. Comput. 3, 93 (1993), DOI: 10.1142/S0218126693000071. Link, ISI, Google Scholar
W. H. Deng and C. P. Li, Physica A 353, 61 (2005), DOI: 10.1016/j.physa.2005.01.021. Crossref, ISI, Google Scholar
W. Deng, C. Li and J. Lü, Nonlin. Dyn. 48, 409 (2007), DOI: 10.1007/s11071-006-9094-0. Crossref, ISI, Google Scholar
S. Deriviěre and M. A. Aziz-Alaoui, Dyn. Contin. Discr. Impul. Syst. Series B: Appl. Algorith. 10, 833 (2003). Google Scholar
Z. M. Ge and C. Y. Ou, Chaos Solit. Fract. 34, 262 (2007), DOI: 10.1016/j.chaos.2005.11.059. Crossref, ISI, Google Scholar
R. Gorenflo and F. Mainardi, Fractals and Fractional Calculus, eds. A. Carpinteri and F. Mainardi (1997) pp. 223–276. Crossref, Google Scholar
I. Grigorenko and E. Grigorenko, Phys. Rev. Lett. 91, 034101 (2003), DOI: 10.1103/PhysRevLett.91.034101. Crossref, ISI, Google Scholar
T. Hartley, C. Lorenzo and H. Qammer, IEEE Trans. CAS-I 42, 485 (1995), DOI: 10.1109/81.404062. Crossref, Google Scholar
R. Hilfer , Applications of Fractional Calculus in Physics ( World Scientific , NJ , 2000 ) . Link, Google Scholar
A. Huang, L. Pivka and C. W. Wu, Int. J. Bifurcation and Chaos 6, 2175 (1996). Link, ISI, Google Scholar
C. Li and G. Chen, Physica A 341, 55 (2004), DOI: 10.1016/j.physa.2004.04.113. Crossref, ISI, Google Scholar
C. Li and G. Chen, Chaos Solit. Fract. 22, 549 (2004), DOI: 10.1016/j.chaos.2004.02.035. Crossref, ISI, Google Scholar
C. Li and G. Peng, Chaos Solit. Fract. 22, 443 (2004), DOI: 10.1016/j.chaos.2004.02.013. Crossref, ISI, Google Scholar
C. Li and T. Zhou, Physica D 212, 111 (2005). ISI, Google Scholar
C. Li and J. Yan, Chaos Solit. Fract. 32, 751 (2007), DOI: 10.1016/j.chaos.2005.11.020. Crossref, ISI, Google Scholar
C. G. Li, X. X. Liao and J. B. Yu, Phys. Rev. E 68, 067203 (2003), DOI: 10.1103/PhysRevE.68.067203. Crossref, ISI, Google Scholar
C. P. Li, W. H. Deng and D. Xu, Physica A 360, 171 (2006), DOI: 10.1016/j.physa.2005.06.078. Crossref, ISI, Google Scholar
J. G. Lu and G. Chen, Chaos Solit. Fract. 27, 685 (2006), DOI: 10.1016/j.chaos.2005.04.037. Crossref, ISI, Google Scholar
D. Matignon, Stability results of fractional differential equations with applications to control processing, Proc. IMACS, IEEE-SMC (1996) pp. 963–968. Google Scholar
K. B. Oldham and J. Spanier , The Fractional Calculus ( Academic Press , NY , 1974 ) . Google Scholar
E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990), DOI: 10.1103/PhysRevLett.64.1196. Crossref, ISI, Google Scholar
L. M. Pecora and T. L. Carrol, Phys. Rev. Lett. 64, 821 (1990), DOI: 10.1103/PhysRevLett.64.821. Crossref, ISI, Google Scholar
G. Peng, Phys. Lett. A 363, 426 (2007), DOI: 10.1016/j.physleta.2006.11.053. Crossref, ISI, Google Scholar
I. Petráš, Chaos Solit. Fract. 38, 140 (2008), DOI: 10.1016/j.chaos.2006.10.054. Crossref, Google Scholar
I. Podlubny , Fractional Differential Equations ( Academic Press , NY , 1999 ) . Google Scholar
O. E. Rössler, Phys. Lett. A 57, 397 (1976), DOI: 10.1016/0375-9601(76)90101-8. Crossref, ISI, Google Scholar
L. J. Sheuet al., Chaos Solit. Fract. 31, 1203 (2007), DOI: 10.1016/j.chaos.2005.10.073. Crossref, ISI, Google Scholar
J. Wang, X. Xiong and Y. Zhang, Physica A 370, 279 (2006), DOI: 10.1016/j.physa.2006.03.021. Crossref, ISI, Google Scholar
X. Wu, J. Li and G. J. Chen, J. Franklin Instit. 345, 392 (2008), DOI: 10.1016/j.jfranklin.2007.11.003. Crossref, ISI, Google Scholar
T. Yamada and H. Fujisaka, Prog. Theoret. Phys. 70, 1240 (1983), DOI: 10.1143/PTP.70.1240. Crossref, Google Scholar
J. Yan and C. Li, Chaos Solit. Fract. 32, 725 (2007), DOI: 10.1016/j.chaos.2005.11.062. Crossref, ISI, Google Scholar
Y. Yu and H. Li, Physica A 387, 1393 (2008), DOI: 10.1016/j.physa.2007.10.052. Crossref, ISI, Google Scholar
S. Zhouet al., Chaos Solit. Fract. 36, 973 (2008), DOI: 10.1016/j.chaos.2006.07.033. Crossref, ISI, Google Scholar
H. Zhu, S. Zhou and J. Zhang, Chaos Solit. Fract. 39, 1595 (2009), DOI: 10.1016/j.chaos.2007.06.082. Crossref, ISI, Google Scholar

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Received 25 February 2008

Revised 11 May 2009

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SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL

Abstract

References

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