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Sliding mode control method is used to study the synchronization of regular network. The method is extended from the single chaos control or synchronization between two chaotic systems to the synchronization of complex network. The sliding surface of the network and the control input are designed. Furthermore, the effectiveness of the method is analyzed based on the stability theory. The Duffing system and the Coullet system are taken as network nodes of the regular network, and the simulation is made to verify the method.
[1] Naseh M R, Haeri M 2009 Chaos, Solitons and Fractals 39 196
[2] Shtessel Y, Kaveh P, Ashrafi A 2009 Journal of the Franklin Institute 346 872
[3] Qi D L, Yang J, Zhang J L 2010 Chin. Phys. B 19 100506
[4] Yau H T, Wang C C, Hsieh C T, Cho C C 2011 Comput. Math. Appl. 61 1912
[5] Chen D Y, Shen T, Mao X Y 2011 Acta Phys. Sin. 60 050505 (in Chinese) [陈帝伊, 申滔, 马孝义 2011 60 050505]
[6] Vasegh N, Khellat F 2009 Chaos, Solitons and Fractals 42 1054
[7] Zribi M, Smaoui N, Salim H 2009 Chaos, Solitons and Fractals 42 3197
[8] Li M, Liu C X 2010 Chin. Phys. B 19 100504
[9] Yu Y, Mi Z Q, Liu X J 2011 Acta Phys. Sin. 60 070509[余洋、米增强、刘兴杰2011 60 070509]
[10] Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才, 宋佳秋 2011 57 4729]
[11] Li D, Leyva I, Almendral J A, Sendiña-Nadal I, Buldú J M, Havlin S, Boccaletti S 2008 Phys. Rev. Lett. 101 168701
[12] Pisarchik A N, Jaimes-Reátegui R, Sevilla-Escoboza R, Boccaletti S 2009 Phys. Rev. E 79 55202
[13] Batista C A S, Batista A M, de Pontes J C A, Lopes S R, Viana R L 2009 Chaos, Solitons and Fractals 41 2220
[14] Kouvaris N, Provata A, Kugiumtzis D 2010 Phys. Lett. A 374 507
[15] Song Q, Cao J D, Liu F 2010 Phys. Lett. A 374 544
[16] Ji D H, Park J H, Yoo W J, Won S C, Lee S M 2010 Phys. Lett. A 374 1218
[17] Liu T, Zhao J, Hill D J 2009 Chaos, Solitons and Fractals 40 1506
[18] Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 27201
[19] Lü L, Li G, Guo L, Meng L, Zou J R, Yang M 2010 Chin. Phys. B 19 080507
[20] Liu H, Chen J, Lu J A, Cao M 2010 Physica A 389 1759
[21] Slotine J E, Li W 1991 Applied Nonlinear Control (Englewood Cliffs, New Jersey: Prentice-Hall)
[22] Wembe E T, Yamapi R 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 1439
[23] Wu C W, Chua L O 1996 Int. J. Bifur. Chaos 6 801
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[1] Naseh M R, Haeri M 2009 Chaos, Solitons and Fractals 39 196
[2] Shtessel Y, Kaveh P, Ashrafi A 2009 Journal of the Franklin Institute 346 872
[3] Qi D L, Yang J, Zhang J L 2010 Chin. Phys. B 19 100506
[4] Yau H T, Wang C C, Hsieh C T, Cho C C 2011 Comput. Math. Appl. 61 1912
[5] Chen D Y, Shen T, Mao X Y 2011 Acta Phys. Sin. 60 050505 (in Chinese) [陈帝伊, 申滔, 马孝义 2011 60 050505]
[6] Vasegh N, Khellat F 2009 Chaos, Solitons and Fractals 42 1054
[7] Zribi M, Smaoui N, Salim H 2009 Chaos, Solitons and Fractals 42 3197
[8] Li M, Liu C X 2010 Chin. Phys. B 19 100504
[9] Yu Y, Mi Z Q, Liu X J 2011 Acta Phys. Sin. 60 070509[余洋、米增强、刘兴杰2011 60 070509]
[10] Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才, 宋佳秋 2011 57 4729]
[11] Li D, Leyva I, Almendral J A, Sendiña-Nadal I, Buldú J M, Havlin S, Boccaletti S 2008 Phys. Rev. Lett. 101 168701
[12] Pisarchik A N, Jaimes-Reátegui R, Sevilla-Escoboza R, Boccaletti S 2009 Phys. Rev. E 79 55202
[13] Batista C A S, Batista A M, de Pontes J C A, Lopes S R, Viana R L 2009 Chaos, Solitons and Fractals 41 2220
[14] Kouvaris N, Provata A, Kugiumtzis D 2010 Phys. Lett. A 374 507
[15] Song Q, Cao J D, Liu F 2010 Phys. Lett. A 374 544
[16] Ji D H, Park J H, Yoo W J, Won S C, Lee S M 2010 Phys. Lett. A 374 1218
[17] Liu T, Zhao J, Hill D J 2009 Chaos, Solitons and Fractals 40 1506
[18] Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 27201
[19] Lü L, Li G, Guo L, Meng L, Zou J R, Yang M 2010 Chin. Phys. B 19 080507
[20] Liu H, Chen J, Lu J A, Cao M 2010 Physica A 389 1759
[21] Slotine J E, Li W 1991 Applied Nonlinear Control (Englewood Cliffs, New Jersey: Prentice-Hall)
[22] Wembe E T, Yamapi R 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 1439
[23] Wu C W, Chua L O 1996 Int. J. Bifur. Chaos 6 801
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