Modified impulsive synchronization of fractional order hyperchaotic systems

doi:10.1088/1674-1056/20/12/120508

Abstract In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.

Keywords: hyperchaotic systems fractional order chaotic systems synchronization impulsive control

Received: 03 July 2011
Revised: 27 July 2011
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Jn	(High-dimensional chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 50830202 and 51073179), the Natural Science Foundation of Chongqing, China (Grant No. CSTC 2010BB2238), the Doctoral Program of Higher Education Foundation of Institutions of China (Grant Nos. 20090191110011 and 20100191120025), the Natural Science Foundation for Postdoctoral Scientists of China (Grant Nos. 20100470813 and 20100480043), and the Fundamental Research Funds for the Central Universities (Grant Nos. CDJZR11 12 00 03 and CDJZR11 12 88 01).

Cite this article:

Fu Jie(浮洁), Yu Miao(余淼), and Ma Tie-Dong(马铁东) Modified impulsive synchronization of fractional order hyperchaotic systems 2011 Chin. Phys. B 20 120508

[1]	Podlubny I 1999 Fractional Differential Equations (New York: Academic)
[2]	Hilfer R 2001 Applications of Fractional Calculus in Physics (Singapore: World Scientific)
[3]	Hartley T T, Lorenzo C F and Qammer H K 1995 emph IEEE Transactions CAS-I 42 485
[4]	Ahmad W M and Sprott J C 2003 emph Chaos, Solitons and Fractals 16 339
[5]	Zhang R X and Yang S P 2009 emph Chin. Phys. B 18 3295
[6]	Lu J G and Chen G R 2006 emph Chaos, Solitons and Fractals 27 685
[7]	Lu J G 2006 emph Phys. Lett. A 354 305
[8]	Li C G and Chen G R 2004 emph Physica A 341 55
[9]	Wu Z M and Xie J Y 2007 emph Chin. Phys. 16 1901
[10]	Pecora L M and Carroll T L 1990 emphPhys. Rev. Lett. 64 821
[11]	Bhalekar S and Daftardar-Gejji V 2010 emph Commun. Nonlinear Sci. Numer. Simul. 15 3536
[12]	Taghvafard H and Erjaee G H 2011 emph Commun. Nonlinear Sci. Numer. Simul. 16 4079
[13]	Hosseinnia S H, Ghaderi R, Ranjbar N A, Mahmoudiana M and Momani S 2010 emph Comput. Math. Appl. 59 1637
[14]	Tavazoei M S and Haeri M 2008 emph Physica A 387 57
[15]	Sun N, Zhang H G and Wang Z L 2011 emph Acta Phys. Sin. 60 050511 (in Chinese)
[16]	Zhao L D, Hu J B and Liu X H 2010 emphActa Phys. Sin. 59 2305 (in Chinese)
[17]	Odibat Z M 2010 emph Nonlinear Dyn. 60 479
[18]	Zhang R X and Yang S P 2010 emph Chin. Phys. B 19 020510
[19]	Wu C J, Zhang Y B and Yang N N 2011 emph Chin. Phys. B 20 060505
[20]	Wang X Y, Zhang Y L, Li D and Zhang N 2011 emph Chin. Phys. B 20 030506
[21]	Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H and Chen H K 2009 emph Int. J. Nonlinear Sci. Numer. Simul. 10 33
[22]	Zhang H G, Ma T D, Huang G B and Wang Z L 2010 emphIEEE Trans. Syst. Man Cybern. B 40 831
[23]	Ma T D, Fu J and Sun Y 2010 emph Chin. Phys. B 19 090502
[24]	Ma T D, Zhang H G and Wang Z L 2007 emphActa Phys. Sin. 56 3796 (in Chinese)
[25]	Zhang H G, Ma T D, Yu W and Fu J 2008 emphChin. Phys. B 17 3616
[26]	Zhang H G, Ma T D, Fu J and Tong S C 2009 emphChin. Phys. B 18 3742
[27]	Zhang H G, Ma T D, Fu J and Tong S C 2009 emphChin. Phys. B 18 3751
[28]	Wang X Y and Song J M 2009 emph Commun. Nonlinear Sci. Numer. Simul. 14 3351
[29]	Gao T G, Chen Z Q, Yuan Z Z and Yu D C 2007 emphChaos, Solitons and Fractals 33 922
[30]	Cafagna D and Grassi G 2010 emphInt. J. Bifur. Chaos 20 3209
[31]	Min F H, Yu Y and Ge C J 2009 emphActa Phys. Sin. 58 1456 (in Chinese)

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Modified impulsive synchronization of fractional order hyperchaotic systems

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