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This article treats the modified function projective synchronization between the hyperchaotic Lorenz-Stenflo(LS) system and a novel hyperchaotic CYQY system, and also that between the LS system and hyperchaotic Chen system, which have completely unknown parameters. By utilizing Lyapunov stability theory and active control method, the adaptive controllers and parameter update laws are derived to make the states of different hyperchaotic systems to attain adaptive modified function projective synchronization. The systems unknown parameters can be identified simultaneously. Numerical simulations are presented to demonstrate the effectiveness of the proposed methods.
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Keywords:
- modified function projective synchronization /
- hyperchaotic system /
- Lyapunov stability theory /
- adaptive control
[1] ［1］Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] ［2］Chen M, Han Z 2003 Chaos Soliton. Fract. 17 709
[3] ［3］Yan J P, Li C P 2005 Chaos Soliton. Fract. 26 1119
[4] ［4］Li C P, Yan J P 2006 Chaos Soliton. Fract. 30 140
[5] ［5］Li G H 2006 Chaos Soliton. Fract. 30 77
[6] ［6］Li G H 2007 Chaos Soliton. Fract. 32 1786
[7] ［7］Wang F Q, Liu C H 2006 Chin. Phys. 15 963
[8] ［8］Zhang Q J, Lu J A 2008 Chaos Soliton. Fract. 37 175
[9] ［9］Du H Y, Zeng Q S, Wang C H 2009 Chaos Soliton. Fract. 42 2399
[10] ］Du H Y, Zeng Q S, Wang C H 2008 Phys. Lett. A 372 5402
[11] ］Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese) ［蔡娜、井元伟、张嗣瀛 2009 58 802］
[12] ］Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) ［王兴元、武相军 2006 55 605］
[13] ］Min F H, Wang Z Q 2007 Acta Phys. Sin. 56 6238 (in Chinese) ［闵富红、王执铨 2007 56 6238］
[14] ］Li S, Xu W, Li R H, Li Y P 2006 Acta Phys. Sin. 55 5681 (in Chinese) ［李爽、徐伟、李瑞红、李玉鹏 2006 55 5681］
[15] ］Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese) ［刘扬正、姜长生、林长圣 2007 56 707］
[16] ］Park J H 2005 Chaos Soliton. Fract. 25 333
[17] ］Park J H 2005 Chaos Soliton. Fract. 26 959
[18] ］Ho M C, Hung Y C, Liu Z Y, Jiang I M 2006 Phys. Lett. A 348 251
[19] ］Al-sawalha M Mossa, Noorani M S M 2009 Commun. Nonlinear. Sci. Numer. Simul. 15 1036
[20] ］Wang X Y, Meng J 2007 Acta Phys. Sin. 56 0802 (in Chinese) ［王兴元、孟娟 2007 56 6288］
[21] ］Stenflo L 1996 Phys. Scr. 53 83
[22] ］Chen Z, Yang Y, Qi Q, Yuan Z 2007 Phys. Lett. A 360 696
[23] ］Gao T, Chen G, Chen Z, Cang S 2007 Phys. Lett. A 361 78
[24] ］Huang J 2008 Phys. Lett. A 362 4799
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[1] ［1］Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] ［2］Chen M, Han Z 2003 Chaos Soliton. Fract. 17 709
[3] ［3］Yan J P, Li C P 2005 Chaos Soliton. Fract. 26 1119
[4] ［4］Li C P, Yan J P 2006 Chaos Soliton. Fract. 30 140
[5] ［5］Li G H 2006 Chaos Soliton. Fract. 30 77
[6] ［6］Li G H 2007 Chaos Soliton. Fract. 32 1786
[7] ［7］Wang F Q, Liu C H 2006 Chin. Phys. 15 963
[8] ［8］Zhang Q J, Lu J A 2008 Chaos Soliton. Fract. 37 175
[9] ［9］Du H Y, Zeng Q S, Wang C H 2009 Chaos Soliton. Fract. 42 2399
[10] ］Du H Y, Zeng Q S, Wang C H 2008 Phys. Lett. A 372 5402
[11] ］Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese) ［蔡娜、井元伟、张嗣瀛 2009 58 802］
[12] ］Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) ［王兴元、武相军 2006 55 605］
[13] ］Min F H, Wang Z Q 2007 Acta Phys. Sin. 56 6238 (in Chinese) ［闵富红、王执铨 2007 56 6238］
[14] ］Li S, Xu W, Li R H, Li Y P 2006 Acta Phys. Sin. 55 5681 (in Chinese) ［李爽、徐伟、李瑞红、李玉鹏 2006 55 5681］
[15] ］Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese) ［刘扬正、姜长生、林长圣 2007 56 707］
[16] ］Park J H 2005 Chaos Soliton. Fract. 25 333
[17] ］Park J H 2005 Chaos Soliton. Fract. 26 959
[18] ］Ho M C, Hung Y C, Liu Z Y, Jiang I M 2006 Phys. Lett. A 348 251
[19] ］Al-sawalha M Mossa, Noorani M S M 2009 Commun. Nonlinear. Sci. Numer. Simul. 15 1036
[20] ］Wang X Y, Meng J 2007 Acta Phys. Sin. 56 0802 (in Chinese) ［王兴元、孟娟 2007 56 6288］
[21] ］Stenflo L 1996 Phys. Scr. 53 83
[22] ］Chen Z, Yang Y, Qi Q, Yuan Z 2007 Phys. Lett. A 360 696
[23] ］Gao T, Chen G, Chen Z, Cang S 2007 Phys. Lett. A 361 78
[24] ］Huang J 2008 Phys. Lett. A 362 4799
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