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Based on Lyapunov stability theory,a simple adaptive scalar controller was designed to realize the anti-synchronization of 3-D quadratic autonomous systems with known or unknown parameters. Furthermore,all the unknown parameters can be estimated dynamically from the time series of the drive and response systems. Numerical simulations show the effectiveness and feasibility of the proposed method.
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Keywords:
- anti-synchronization /
- 3-D quadratic autonomous chaos systems /
- scalar controller /
- Lyapunov function
[1] Pecora L M,Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Chen G R,Dong X 1998 From Chaos to Order:Methodologies,Perspectives,and Applications,(Singapore:World Scientific Pub. Co.)
[3] 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]
[4] Li F,Hu A H,Xu Z Y 2006 Chin. Phys. 15 507
[5] Li R H,Xu W,Li S 2007 Chin. Phys. 16 1591
[6] Li X C,Xu W,Xiao Y Z 2008 Acta Phys. Sin. 57 1457 (in Chinese) [李秀春、徐 伟、肖玉柱 2008 57 1457]
[7] Liu W Q,Xiao J H,Qiao X L,Yang J Z 2006 Phys. Rev. E 73 057203
[8] Belykh V N,Chua L O 1992 Int. J. Bifur. Chaos 2 697
[9] Huygens C 1669 Philos. R. Soc. London 4 937
[10] Bennett M,Schatz M F,Rockwood H,Wiesenfeld K 2002 Proc. R. Soc. A 458 563
[11] Kim C M,Rim S H,Key W 2003 Phys. Lett. A 320 39
[12] Cao L Y,Lai Y C 1998 Phys. Rev. E 58 382
[13] Wang X Y,Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元、王明军 2007 56 6843]
[14] Liu F C,Zang X F,Song J Q 2009 Acta Phys. Sin. 58 3765 (in Chinese) [刘福才、臧秀凤、宋佳秋 2009 58 3765]
[15] Li R H,Xu W,Li S 2009 Chaos,Solitons & Fractals 40 1288
[16] Al-Sawalha M M,Noorani M S M 2008 Chaos,Solitons & Fractals 42 170
[17] Wang L 2009 Chaos 19 013107
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[1] Pecora L M,Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Chen G R,Dong X 1998 From Chaos to Order:Methodologies,Perspectives,and Applications,(Singapore:World Scientific Pub. Co.)
[3] 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]
[4] Li F,Hu A H,Xu Z Y 2006 Chin. Phys. 15 507
[5] Li R H,Xu W,Li S 2007 Chin. Phys. 16 1591
[6] Li X C,Xu W,Xiao Y Z 2008 Acta Phys. Sin. 57 1457 (in Chinese) [李秀春、徐 伟、肖玉柱 2008 57 1457]
[7] Liu W Q,Xiao J H,Qiao X L,Yang J Z 2006 Phys. Rev. E 73 057203
[8] Belykh V N,Chua L O 1992 Int. J. Bifur. Chaos 2 697
[9] Huygens C 1669 Philos. R. Soc. London 4 937
[10] Bennett M,Schatz M F,Rockwood H,Wiesenfeld K 2002 Proc. R. Soc. A 458 563
[11] Kim C M,Rim S H,Key W 2003 Phys. Lett. A 320 39
[12] Cao L Y,Lai Y C 1998 Phys. Rev. E 58 382
[13] Wang X Y,Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元、王明军 2007 56 6843]
[14] Liu F C,Zang X F,Song J Q 2009 Acta Phys. Sin. 58 3765 (in Chinese) [刘福才、臧秀凤、宋佳秋 2009 58 3765]
[15] Li R H,Xu W,Li S 2009 Chaos,Solitons & Fractals 40 1288
[16] Al-Sawalha M M,Noorani M S M 2008 Chaos,Solitons & Fractals 42 170
[17] Wang L 2009 Chaos 19 013107
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