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Generalized synchronization of chaos is studied for two-dimensional time-delayed chaotic systems with different structurs. The auxiliary system method and the stability theory of functional differential equations are used. Compared with the conventional generalized synchronization approaches, the proposed method is convenient to realize generalized synchronization of chaos. Simulation results illustrate the validity of the method.
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Keywords:
- two-dimensional time-delayed chaotic systems /
- generalized synchronization of chaos /
- auxiliary system method
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Carroll T L, Pecora L M 1991 IEEE Trans. Circuit Syst. 38 453
[3] Kocarev L, Parlitz U 1995 Phys. Rev. Lett. 74 5208
[4] Pyragas K.1993 Phys. Lett. A 181 203
[5] Zhang R X, Yang S P 2010 Chin. Phys. B 19 20510
[6] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[7] Yue L J, Chen Y Y, Peng J H 2001 Acta Phys. Sin. 50 2097 (in Chinese) [岳丽娟、 陈艳艳、 彭建华 2001 50 2097]
[8] Yang L B, Yang T 2000 Acta Phys. Sin. 49 33 (in Chinese) [杨林保、 杨 涛 2000 49 33]
[9] Kocarev L, Parlitz U 1996 Phys. Rev. Lett. 76 1816
[10] Rulkov N F, Sushchik M M , Tsimring L S ,Abarbanel H D I 1995 Phys. Rev. E 51 980
[11] Li G H 2004 Acta Phys. Sin. 53 999 (in Chinese) [李国辉 2004 53 999]
[12] Wu Z Q, Kuang Y 2009 Acta Phys. Sin. 58 6823 (in Chinese) [吴忠强、 邝 钰 2009 58 6823]
[13] Guo L X, Xu Z Y 2008 Acta Phys. Sin. 57 6823 (in Chinese) [过榴晓、 徐振源 2008 57 6823]
[14] Hu A H, Xu Z Y, Guo L X 2009 Acta Phys. Sin. 58 6030 (in Chinese) [胡爱花、 徐振源、 过榴晓 2009 58 6030]
[15] Mackey M, Glass L 1977 Science 197 287
[16] Anindita T, Poria S, Chatterjee P 2009 Chaos,Solitons and Fractals 41 190
[17] Ghose D, Saha P, Chowdhury A R 2010 Commom Nonlinear Sci Number Simulat 15 1640
[18] Ge Z M, Wong Y T, Li S Y 2008 Journal of Sound and Vibration 318 267
[19] Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147 (in Chinese) [张化光、 马大中、 王占山、 冯 建 2010 59 147]
[20] Qi W, Wang Y H 2009 Chin. Phys. B 18 1404
[21] Shu Y L 2004 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [舒永录 2004 博士论文 (重庆: 重庆大学)]
[22] Abarbanel H D I, Rulkow N F, Sushchik M M 1996 Phys. Rev. E 53 4528
[23] Zhang X M 2004 MS Thesis (Changchun: Northeast Normal University) (in Chinese) [张晓明 2004 硕士学位论文 (长春: 东北师范大学)]
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Carroll T L, Pecora L M 1991 IEEE Trans. Circuit Syst. 38 453
[3] Kocarev L, Parlitz U 1995 Phys. Rev. Lett. 74 5208
[4] Pyragas K.1993 Phys. Lett. A 181 203
[5] Zhang R X, Yang S P 2010 Chin. Phys. B 19 20510
[6] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[7] Yue L J, Chen Y Y, Peng J H 2001 Acta Phys. Sin. 50 2097 (in Chinese) [岳丽娟、 陈艳艳、 彭建华 2001 50 2097]
[8] Yang L B, Yang T 2000 Acta Phys. Sin. 49 33 (in Chinese) [杨林保、 杨 涛 2000 49 33]
[9] Kocarev L, Parlitz U 1996 Phys. Rev. Lett. 76 1816
[10] Rulkov N F, Sushchik M M , Tsimring L S ,Abarbanel H D I 1995 Phys. Rev. E 51 980
[11] Li G H 2004 Acta Phys. Sin. 53 999 (in Chinese) [李国辉 2004 53 999]
[12] Wu Z Q, Kuang Y 2009 Acta Phys. Sin. 58 6823 (in Chinese) [吴忠强、 邝 钰 2009 58 6823]
[13] Guo L X, Xu Z Y 2008 Acta Phys. Sin. 57 6823 (in Chinese) [过榴晓、 徐振源 2008 57 6823]
[14] Hu A H, Xu Z Y, Guo L X 2009 Acta Phys. Sin. 58 6030 (in Chinese) [胡爱花、 徐振源、 过榴晓 2009 58 6030]
[15] Mackey M, Glass L 1977 Science 197 287
[16] Anindita T, Poria S, Chatterjee P 2009 Chaos,Solitons and Fractals 41 190
[17] Ghose D, Saha P, Chowdhury A R 2010 Commom Nonlinear Sci Number Simulat 15 1640
[18] Ge Z M, Wong Y T, Li S Y 2008 Journal of Sound and Vibration 318 267
[19] Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147 (in Chinese) [张化光、 马大中、 王占山、 冯 建 2010 59 147]
[20] Qi W, Wang Y H 2009 Chin. Phys. B 18 1404
[21] Shu Y L 2004 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [舒永录 2004 博士论文 (重庆: 重庆大学)]
[22] Abarbanel H D I, Rulkow N F, Sushchik M M 1996 Phys. Rev. E 53 4528
[23] Zhang X M 2004 MS Thesis (Changchun: Northeast Normal University) (in Chinese) [张晓明 2004 硕士学位论文 (长春: 东北师范大学)]
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