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A new switched four-scroll hyperchaotic system with two subsystems which are interconnected and can be switched to each other, is generated. The two subsystems are analyzed in detail by presenting the bifurcation diagram, the feature of equilibrium, the phase portraits of chaotic attractor, the Lyapunov exponent and the evolution course of the dynamical action. A practical circuit is designed to conveniently realize two subsystems for the hyperchaotic systems each with only smooth quadratic nonlinearity. Based on time-dependent switching law and state-dependent switching law, the two subsystems can be switched from one to another either randomly or independently, just by using this special circuit.
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Keywords:
- switching /
- four-scroll chaotic attractor /
- hyperchaotic system /
- switching law
[1] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[2] Liu W B, Chen G R 2004 Int. J. Bifur. Chaos 14 1395
[3] Liu W B, Tang K S,Chen G R 2007 Int. J. Bifur. Chaos 17 4153
[4] Qiao X H, Bao B C 2009 Acta Phys. Sin. 58 8152 (in Chinese) [乔晓华、 包伯成 2009 物理学报 58 8152]
[5] Yu S M, Ma Z G, Qiu S S, Peng S G, Lin Q H 2004 Chin. Phys. B 13 317
[6] Yu S M, Qiu S S 2004 Acta Electron. Sin. 32 814 (in Chinese) [禹思敏、 丘水生 2004 电子学报 32 814]
[7] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞、 禹思敏 2009 物理学报 58 120]
[8] Lü J H 2006 IEEE Trans. Circuits Syst. Ⅰ 53 1596
[9] Lü J H, Yu S M, Chen G R 2006 IEEE Trans. Circuits Syst. Ⅰ 53 149
[10] Wang F Q, Liu C X 2007 Chin. Phys. B 16 942
[11] Luo X H, Li H Q, Dai X G 2008 Acta Phys. Sin. 57 7511 (in Chinese) [罗小华、 李华青、 代祥光 2008 物理学报 57 7511]
[12] Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 58 3337 (in Chinese) [谌 龙、 彭海军、 王德石 2008 物理学报 57 3337]
[13] Qi G Y 2006 Int. J. Bifur. Chaos 16 859
[14] Zhang Y H, Qi G Y, Liu W L, Yan Y 2006 Acta Phys. Sin. 55 3307 (in Chinese) [张宇辉 、 齐国元、 刘文良、 阎 彦 2006 物理学报 55 3307]
[15] Wang F Z, Qi G Y, Chen Z Q, Yuan Z Z 2007 Acta Phys. Sin. 56 3137 (in Chinese) [王繁珍、 齐国元、 陈增强、 袁著祉 2007 物理学报 56 3137]
[16] Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 物理学报 58 3734]
[17] Lü J H, Chen G 2006 Int. J. Bifur. Chaos 16 775
[18] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 物理学报 58 8139]
[19] Lü J H, Yu X, Chen G 2003 IEEE Trans. Circuits Syst. Ⅰ 50 198
[20] Zhang Y J, Wang C P, Wang G Y, Xu N, Wang Z L 2009 J. China Univ. Posts Telecom. 16 122
[21] Liu Y Z, Jiang C S 2009 Acta Phys. Sin. 58 771 (in Chinese) [刘扬正、 姜长生 2009 物理学报 58 771]
[22] Wang Z L, Liu B, Wang S B 2009 Periodic. Ocean Univ. China (Nat. Sci. Ed.) 39 509 (in Chinese) [王忠林、 刘 滨、 王树斌 2009 中国海洋大学学报 (自然科学版) 39 509]
[23] Wang C P, Wang G Y 2009 J. Hangzhou Dianzi Univ. 29 28 (in Chinese) [王翠平、 王光义 2009 杭州电子科技大学学报 29 28]
[24] Lin C X, Hao J H 2008 J. Dyn. Contr. 6 254 (in Chinese) [林彩霞、 郝建红 2008 动力学与控制学报 6 254]
[25] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 3107 (in Chinese) [刘扬正、 姜长生、 林长圣 2007 物理学报 56 3107]
[26] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 5131 (in Chinese) [刘扬正、 姜长生、 林长圣 2007 物理学报 56 5131]
[27] Cheng D Z, Guo Y Q 2005 Contr. Theory Appl. 22 954 (in Chinese) [程代展、 郭宇骞 2005 控制理论与应用 22 954]
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[1] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[2] Liu W B, Chen G R 2004 Int. J. Bifur. Chaos 14 1395
[3] Liu W B, Tang K S,Chen G R 2007 Int. J. Bifur. Chaos 17 4153
[4] Qiao X H, Bao B C 2009 Acta Phys. Sin. 58 8152 (in Chinese) [乔晓华、 包伯成 2009 物理学报 58 8152]
[5] Yu S M, Ma Z G, Qiu S S, Peng S G, Lin Q H 2004 Chin. Phys. B 13 317
[6] Yu S M, Qiu S S 2004 Acta Electron. Sin. 32 814 (in Chinese) [禹思敏、 丘水生 2004 电子学报 32 814]
[7] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞、 禹思敏 2009 物理学报 58 120]
[8] Lü J H 2006 IEEE Trans. Circuits Syst. Ⅰ 53 1596
[9] Lü J H, Yu S M, Chen G R 2006 IEEE Trans. Circuits Syst. Ⅰ 53 149
[10] Wang F Q, Liu C X 2007 Chin. Phys. B 16 942
[11] Luo X H, Li H Q, Dai X G 2008 Acta Phys. Sin. 57 7511 (in Chinese) [罗小华、 李华青、 代祥光 2008 物理学报 57 7511]
[12] Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 58 3337 (in Chinese) [谌 龙、 彭海军、 王德石 2008 物理学报 57 3337]
[13] Qi G Y 2006 Int. J. Bifur. Chaos 16 859
[14] Zhang Y H, Qi G Y, Liu W L, Yan Y 2006 Acta Phys. Sin. 55 3307 (in Chinese) [张宇辉 、 齐国元、 刘文良、 阎 彦 2006 物理学报 55 3307]
[15] Wang F Z, Qi G Y, Chen Z Q, Yuan Z Z 2007 Acta Phys. Sin. 56 3137 (in Chinese) [王繁珍、 齐国元、 陈增强、 袁著祉 2007 物理学报 56 3137]
[16] Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 物理学报 58 3734]
[17] Lü J H, Chen G 2006 Int. J. Bifur. Chaos 16 775
[18] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 物理学报 58 8139]
[19] Lü J H, Yu X, Chen G 2003 IEEE Trans. Circuits Syst. Ⅰ 50 198
[20] Zhang Y J, Wang C P, Wang G Y, Xu N, Wang Z L 2009 J. China Univ. Posts Telecom. 16 122
[21] Liu Y Z, Jiang C S 2009 Acta Phys. Sin. 58 771 (in Chinese) [刘扬正、 姜长生 2009 物理学报 58 771]
[22] Wang Z L, Liu B, Wang S B 2009 Periodic. Ocean Univ. China (Nat. Sci. Ed.) 39 509 (in Chinese) [王忠林、 刘 滨、 王树斌 2009 中国海洋大学学报 (自然科学版) 39 509]
[23] Wang C P, Wang G Y 2009 J. Hangzhou Dianzi Univ. 29 28 (in Chinese) [王翠平、 王光义 2009 杭州电子科技大学学报 29 28]
[24] Lin C X, Hao J H 2008 J. Dyn. Contr. 6 254 (in Chinese) [林彩霞、 郝建红 2008 动力学与控制学报 6 254]
[25] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 3107 (in Chinese) [刘扬正、 姜长生、 林长圣 2007 物理学报 56 3107]
[26] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 5131 (in Chinese) [刘扬正、 姜长生、 林长圣 2007 物理学报 56 5131]
[27] Cheng D Z, Guo Y Q 2005 Contr. Theory Appl. 22 954 (in Chinese) [程代展、 郭宇骞 2005 控制理论与应用 22 954]
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