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Chua’s circuits are non-smooth systems. At first,by the generalized Hamiltonian system and observer approach,the problem of the chaotic synchronization of Chua’s circuits with nonlinear control is transformed into that of the stability of zero solution of smooth error systems with nonlinear control. Then,the sliding mode control is applied to the error systems, which stabilizes their zero solutions,and the synchronization conditions are obtained. At last,the numerical results are shown to be in very good agreement with the theoretical analysis.
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Keywords:
- Chua’s circuit /
- chaotic synchronization /
- generalized Hamiltonian system /
- sliding mode control
[1] Boccaletti S,Kurths J,Osipov G,Valladares D L,Zhou C S 2002 Phys. Rep. 366 1
[2] Cai G L,Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、 黄娟娟 2006 55 3997]
[3] Wang X Y,Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) [王兴元、武相军 2006 55 605]
[4] Cheng J F,Zhang R Y,Peng J H 2003 Acta Phys. Sin. 52 1589 (in Chinese) [陈菊芳、 张入元、 彭建华 2003 52 1589]
[5] Guan X P,He Y H,Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平、 何宴辉、 范正平 2003 52 276]
[6] Y ang T,Shao H H 2002 Acta Phys . Sin. 51 742 (in Chinese) [杨 涛、 邵惠鹤 2002 51 742 ]
[7] Gámez-Guzmán L,Cruz-Hernández C,López-Gutiérrez R M,García Guerrero E E 2009 Commun Nonlinear Sci Numer Simulat 14 2765
[8] Agiza H N,Matouk A E 2006 Chaos, Solitons and Fract. 28 219
[9] Li W L,Chen X Q 2009 Commun Nonlinear Sci Numer Simulat 14 3100
[10] Hu J,Chen S H,Chen L 2005 Phys. Lett. A 339 455
[11] Yan J J,Lin J S,Liao T L 2008 Chaos, Solitons and Fract. 36 45
[12] Li X C,Xu W,Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese) [李秀春、徐 伟、肖玉柱 2008 57 4721]
[13] Sira-Ramírez H,Cruz H 2001 Int. J. Bifurcat. Chaos 11 1381
[14] Liu D,Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese) [刘 丁、闫晓妹 2008 58 3747]
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[1] Boccaletti S,Kurths J,Osipov G,Valladares D L,Zhou C S 2002 Phys. Rep. 366 1
[2] Cai G L,Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、 黄娟娟 2006 55 3997]
[3] Wang X Y,Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) [王兴元、武相军 2006 55 605]
[4] Cheng J F,Zhang R Y,Peng J H 2003 Acta Phys. Sin. 52 1589 (in Chinese) [陈菊芳、 张入元、 彭建华 2003 52 1589]
[5] Guan X P,He Y H,Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平、 何宴辉、 范正平 2003 52 276]
[6] Y ang T,Shao H H 2002 Acta Phys . Sin. 51 742 (in Chinese) [杨 涛、 邵惠鹤 2002 51 742 ]
[7] Gámez-Guzmán L,Cruz-Hernández C,López-Gutiérrez R M,García Guerrero E E 2009 Commun Nonlinear Sci Numer Simulat 14 2765
[8] Agiza H N,Matouk A E 2006 Chaos, Solitons and Fract. 28 219
[9] Li W L,Chen X Q 2009 Commun Nonlinear Sci Numer Simulat 14 3100
[10] Hu J,Chen S H,Chen L 2005 Phys. Lett. A 339 455
[11] Yan J J,Lin J S,Liao T L 2008 Chaos, Solitons and Fract. 36 45
[12] Li X C,Xu W,Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese) [李秀春、徐 伟、肖玉柱 2008 57 4721]
[13] Sira-Ramírez H,Cruz H 2001 Int. J. Bifurcat. Chaos 11 1381
[14] Liu D,Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese) [刘 丁、闫晓妹 2008 58 3747]
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