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Taking hyperchaotic Chen system and hyperchaotic Lorenz system as examples, we study the anti-synchronization of hyperchaotic systems with slow time-varying parameters. Firstly, taking advantage of active control concept, the non-linear parts of hyperchaotic systems are eliminated, and then based on Lyapunov stability theory, a kind of parameter adaptive control law is selected reasonably to achieve anti-synchronization of two hyperchaotic systems, which is a good solution to the time-varying parameters perturbation problem. Furthermore, hyperchaotic systems of different parameters with fractional order are studied via sliding mode control,which is proved to be valid theoretically. Numerical simulation experiments verify the effectiveness and feasibility of the proposed method.
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Keywords:
- hyperchaos /
- fractional order /
- adaptive /
- sliding mode
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Li G H 2005 Chaos, Soliton and Fractals.32 1454
[3] Yin X H, Shan X M, Ren Y 2003 Atomic Energy Science and Technology 37 185 (in Chinese) [尹逊和、山秀明、任 勇 2003 原子能科学技术 37 185]
[4] Liu F C, Liang X M, Song J Q 2008 Acta Phys. Sin. 57 1458 (in Chinese) [刘福才、梁晓明、宋佳秋 2008 物理学报 57 1458]
[5] Dadras S, Momeni H R, Majd V J 2008 Chaos, Soliton and Fractals 41 1857
[6] Tang R A, Liu Y L, Xue J K 2009 Phys. Lett. A 373 1449
[7] Kuntanapreeda S 2009 Phys. Lett. A 373 2837
[8] Wei D Q, Luo X S, Bing H W, Jin Q F 2007 Phys. Lett. A 363 71
[9] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、黄娟娟 2006 物理学报 55 3997]
[10] Jia H Y, Chen Z Q, Yuan Z Z 2010 Chin. Phys.B 19 507
[11] Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys.B 19 509
[12] Sun L, Jiang D P 2006 Acta Phys. Sin. 55 3283 (in Chinese) [孙 琳、姜德平 2006 物理学报 55 3283]
[13] Liu D, Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese) [刘 丁、闫晓妹 2009 物理学报 58 3747]
[14] Yang J, Qi D L 2010 Chin. Phys.B 19 508
[15] Zhang R X, Yang S P 2010 Chin. Phys.B 19 510
[16] Zhang R X, Yang S P 2009 Journal of Hebei Normal University 33 37 (in Chinese) [张若洵、杨世平 2009 河北师范大学学报 33 37]
[17] Hosseinnia SH, Ghaderi R, Ranjbar NA 2010 Comput. Math. Applicat. 59 1637
[18] Xu C, Feng JW,Austin F 2009 Int. J. Nonlin. Sci.10 1517
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Li G H 2005 Chaos, Soliton and Fractals.32 1454
[3] Yin X H, Shan X M, Ren Y 2003 Atomic Energy Science and Technology 37 185 (in Chinese) [尹逊和、山秀明、任 勇 2003 原子能科学技术 37 185]
[4] Liu F C, Liang X M, Song J Q 2008 Acta Phys. Sin. 57 1458 (in Chinese) [刘福才、梁晓明、宋佳秋 2008 物理学报 57 1458]
[5] Dadras S, Momeni H R, Majd V J 2008 Chaos, Soliton and Fractals 41 1857
[6] Tang R A, Liu Y L, Xue J K 2009 Phys. Lett. A 373 1449
[7] Kuntanapreeda S 2009 Phys. Lett. A 373 2837
[8] Wei D Q, Luo X S, Bing H W, Jin Q F 2007 Phys. Lett. A 363 71
[9] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、黄娟娟 2006 物理学报 55 3997]
[10] Jia H Y, Chen Z Q, Yuan Z Z 2010 Chin. Phys.B 19 507
[11] Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys.B 19 509
[12] Sun L, Jiang D P 2006 Acta Phys. Sin. 55 3283 (in Chinese) [孙 琳、姜德平 2006 物理学报 55 3283]
[13] Liu D, Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese) [刘 丁、闫晓妹 2009 物理学报 58 3747]
[14] Yang J, Qi D L 2010 Chin. Phys.B 19 508
[15] Zhang R X, Yang S P 2010 Chin. Phys.B 19 510
[16] Zhang R X, Yang S P 2009 Journal of Hebei Normal University 33 37 (in Chinese) [张若洵、杨世平 2009 河北师范大学学报 33 37]
[17] Hosseinnia SH, Ghaderi R, Ranjbar NA 2010 Comput. Math. Applicat. 59 1637
[18] Xu C, Feng JW,Austin F 2009 Int. J. Nonlin. Sci.10 1517
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