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In order to improve the security of secure communication combined with the generalized dislocated projective synchronization and lag projective synchronization, a new generalized dislocated lag projective synchronization (GDLPS) is investigated. This paper takes the fractional order Chen system and L system as examples. for the parameters of the two systems are uncertain, based on the fractional stability theory and adaptive control method, the nonlinear controller and parameter update laws are designed for the GDLPS between the two chaotic systems with uncertain parameters. Under the controller and parameter update laws, GDLPS of the two uncertain parameters chaotic systems is achieved and all uncertain parameters of the drive system and response system are identified. Theoretical analyses and numerical simulation show that this method is feasible and effective.
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Keywords:
- fractional-order /
- chaotic /
- generalized dislocated lag projective synchronization /
- parameters identification
[1] Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[2] Anastasio T J 1994 Biol. Cybern. 72 69
[3] Bagley R L, Calico R A 1991 J. Guid. Control Dyn. 14 304
[4] Wang Z, Huang X, Shi G D 2011 Comput. Math. Appl. 62 1531
[5] Feki M 2003 Chaos Solitons Fractals 18 141
[6] Wu X J, Wang H, Lu H T 2012 Nonlinear Anal. RWA 13 1441
[7] Xue W, Xu J K, Cang S J, Jia H Y 2014 Chin. Phys. B 23 060501
[8] Rivest R L, Shamir A, Adleman L 1978 Commun. ACM 21 120
[9] Yu S M 2011 Chaotic Systems and Chaotic Circuits: Principle, Design and Its Application in Communications (Xi'an: Xidian University Press) p217 (in Chinese) [禹思敏 2011 混沌系统与混沌电路——原理、设计及其在保密通信中的应用(西安: 西安电子科技大学出版社)第217页]
[10] Endo I, Chua L O 1991 Int. J. Bifurcation Chao 1 701
[11] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[12] Yuan L G, Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 305
[13] Wang X Y, He Y 2008 Phys. Lett. A 372 435
[14] Wang X Y, Zhang Y L 2011 Chin. Phys. B 20 100506
[15] Yang Y H, Xiao J, Ma Z Z 2013 Acta Phys. Sin. 62 180505 (in Chinese) [杨叶红, 肖剑, 马珍珍 2013 物理学报 62 180505]
[16] Zhang Q J, Lu J A 2008 Phys. Lett. A 372 1416
[17] Chai Y, Chen L Q 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3390
[18] Luo C, Wang X Y 2013 J. Vib. Control 20 1831
[19] Chen L P, Chai Y, Wu R C 2011 Phys. Lett. A 375 2099
[20] Wang S, Yu Y G, Wang H, Rahmani A 2014 Chin. Phys. B 23 040502
[21] Agrawal S K, Das S 2013 Nonlinear Dyn. 73 907
[22] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese) [黄丽莲, 齐雪 2013 物理学报 62 080507]
[23] Dong J, Zhang G J, Yao H, Wang J 2013 J. Electron. Inform. Technol. 35 1371 (in Chinese) [董俊, 张广军, 姚宏, 王珏 2013 电子与信息学报 35 1371]
[24] Petrtráš I 2011 Fractional-Order Nonlinear Systems (Beijing: Higher Education Press) p341
[25] Lu J, Chen G 2002 Int. J. Bifurcat. Chaos 12 659
[26] Deng W H, Li C P 2005 Physica A 353 61
[27] Zhao D L, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 物理学报 59 2305]
[28] Diethelm K, Ford N J, Freed A D 2002 Nonlinear Dyn. 29 3
[29] El-Sayed A M A, Ahmed E, Herzallah M A E 2011 J. Fract. Calc. Appl. 1 1
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[1] Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[2] Anastasio T J 1994 Biol. Cybern. 72 69
[3] Bagley R L, Calico R A 1991 J. Guid. Control Dyn. 14 304
[4] Wang Z, Huang X, Shi G D 2011 Comput. Math. Appl. 62 1531
[5] Feki M 2003 Chaos Solitons Fractals 18 141
[6] Wu X J, Wang H, Lu H T 2012 Nonlinear Anal. RWA 13 1441
[7] Xue W, Xu J K, Cang S J, Jia H Y 2014 Chin. Phys. B 23 060501
[8] Rivest R L, Shamir A, Adleman L 1978 Commun. ACM 21 120
[9] Yu S M 2011 Chaotic Systems and Chaotic Circuits: Principle, Design and Its Application in Communications (Xi'an: Xidian University Press) p217 (in Chinese) [禹思敏 2011 混沌系统与混沌电路——原理、设计及其在保密通信中的应用(西安: 西安电子科技大学出版社)第217页]
[10] Endo I, Chua L O 1991 Int. J. Bifurcation Chao 1 701
[11] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[12] Yuan L G, Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 305
[13] Wang X Y, He Y 2008 Phys. Lett. A 372 435
[14] Wang X Y, Zhang Y L 2011 Chin. Phys. B 20 100506
[15] Yang Y H, Xiao J, Ma Z Z 2013 Acta Phys. Sin. 62 180505 (in Chinese) [杨叶红, 肖剑, 马珍珍 2013 物理学报 62 180505]
[16] Zhang Q J, Lu J A 2008 Phys. Lett. A 372 1416
[17] Chai Y, Chen L Q 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3390
[18] Luo C, Wang X Y 2013 J. Vib. Control 20 1831
[19] Chen L P, Chai Y, Wu R C 2011 Phys. Lett. A 375 2099
[20] Wang S, Yu Y G, Wang H, Rahmani A 2014 Chin. Phys. B 23 040502
[21] Agrawal S K, Das S 2013 Nonlinear Dyn. 73 907
[22] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese) [黄丽莲, 齐雪 2013 物理学报 62 080507]
[23] Dong J, Zhang G J, Yao H, Wang J 2013 J. Electron. Inform. Technol. 35 1371 (in Chinese) [董俊, 张广军, 姚宏, 王珏 2013 电子与信息学报 35 1371]
[24] Petrtráš I 2011 Fractional-Order Nonlinear Systems (Beijing: Higher Education Press) p341
[25] Lu J, Chen G 2002 Int. J. Bifurcat. Chaos 12 659
[26] Deng W H, Li C P 2005 Physica A 353 61
[27] Zhao D L, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 物理学报 59 2305]
[28] Diethelm K, Ford N J, Freed A D 2002 Nonlinear Dyn. 29 3
[29] El-Sayed A M A, Ahmed E, Herzallah M A E 2011 J. Fract. Calc. Appl. 1 1
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