摘要Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach.
Abstract:Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach.
FENG Cun-Fang**;WANG Ying-Hai
. Projective Synchronization in Modulated Time-Delayed Chaotic Systems Using an Active Control Approach[J]. 中国物理快报, 2011, 28(12): 120504-120504.
FENG Cun-Fang**, WANG Ying-Hai
. Projective Synchronization in Modulated Time-Delayed Chaotic Systems Using an Active Control Approach. Chin. Phys. Lett., 2011, 28(12): 120504-120504.
[1] Pecora L M and Carroll T C 1990 Phys. Rev. Lett. 64 821
[2] Barahona M and Pecora L M 2002 Phys. Rev. Lett. 89 054101
[3] Amritkar R E and Rangarajan G 2006 Phys. Rev. Lett. 96 258102
[4] Zhou J, Xiang L and Liu Z R 2007 Physica A 385 729
[5] Zhou J, Lu J A and Lü J H 2008 Automatica 44 996
[6] Rulkov N F, Sushchik M M, Tsimring L S and Abarbanel H D I 1995 Phys. Rev. E 51 980
[7] Kadir A, Wang X Y and Zhao Y Z 2011 Chin. Phys. Lett. 28 090503
[8] Rosenblum M G, Pikovsky A S and Kurths J 1996 Phys. Rev. Lett. 76 1804
[9] Zhan M, Wei G W and Lai C H 2002 Phys. Rev. E 65 036202
[10] Voss H U 2001 Phys. Rev. Lett. 87 014102
[11] Mainieri R and Rehacek J 1999 Phys. Rev. Lett. 82 3042
[12] Feng C F, Xu X J, Wang S J and Wang Y H 2008 Chaos 18 023117
Feng C F, Zhang Y, Sun J T, Qi W and Wang Y H 2008 Chaos, Solitons Fractals 38 743
[13] Feng C F 2010 Nonlinear Dyn 62 453
[14] Ghosh D, Banerjee S and Chowdhuryd A R 2010 Phys. Lett. A 374 2143
[15] Wu Z Y and Fu X C 2010 Chin. Phys. Lett. 27 050502
[16] Cao L Y and Lai Y C 1998 Phys. Rev. E 58 382
[17] Chee C Y and Xu D L 2005 Chaos Solitons and Fractals 23 1063
[18] Foss J, Longtin A, Mensour B and Milton J 1996 Phys. Rev. Lett. 76 708
[19] Pyragas K 1998 Phys. Rev. E 58 3067
[20] Pyragas K 1998 Int. J. Bifur. Chaos 8 1839
[21] Banerjee S, Ghosh D, Ray A and Roy-Chowdhury A 2008 Europhys. Lett. 81 20006
[22] Arecchi F T, Meucci R, Allaria E, Garbo A Di and Tsimring L S 2002 Phys. Rev. E 65 046237
[23] Senthilkumar D V and Lakshmanan M 2007 Chaos 17 013112
[24] Hegger R, Bunner M J, Kantz H and Giaquinta A 1998 Phys. Rev. Lett. 81 558
[25] Zhao H, Liu Y W, Wang Y H and Hu B B 1998 Phys. Rev. E 58 4383
[26] Ikeda K, Daido H and Akimoto O 1980 Phys. Rev. Lett. 45 709
[27] Vallée R and Delisle C 1986 Phys. Rev. A 34 309
[28] Goedgebuer J P, Larger L and Porte H 1998 Phys. Rev. E 57 2795
[29] Mackey M C and Glass L 1977 Science 197 287
[30] Feng C F, Zhang Y and Wang Y H 2006 Chin. Phys. Lett. 23 1418
[31] Ho M C, Hung Y C and Chou C H 2002 Phys. Lett. A 296 43
[32] He R and Vaiya P G 1992 Phys. Rev. A 46 7387
[33] Li J N and Hao B L 1989 Commun. Theor. Phys. 11 265