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In this paper we propose a new simple four-dimensional (4D) chaotic system by introducing a nonlinear state feedback controller. There is a fully qualified four-wing type in all directions of the chaotic attractor. With a larger positive Lyapunov exponent, some interesting and complex dynamic behaviors are obtained. Basic dynamical properties of the four-wing attractor are studied by numerical and theoretical analyses, such as dissipativity equilibria, Poincaré map, spectrum map, continuous spectrum and chaotic behaviors. The sensitivities of system parameters to the chaotic behaviors are further explored by calculating, in detail, its Lyapunov exponent spectrum and bifurcation diagrams. Finally, an oscillator circuit is designed for implementation. The EWB observation results are in reasonable agreement with the numerical simulation results.
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Keywords:
- 4-D chaos /
- four-wing chaotic system /
- Poincaré map /
- Lyapunov exponents
[1] 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]
[2] Li Q D, Yang X S Yang F Y 2003 Electron. Lett. 39 1306
[3] Lü J, Chen G, Yu X, Leung H 2004 IEEE Trans. Circuits Syst. I, Reg. Papers 51 2476
[4] Han F, Yu X, Wang Y, Feng Y Chen G 2003 Electron. Lett. 39 1636
[5] Lü J, Han F, Yu X, Chen G 2004 Automatica 40 1677
[6] Yu S, Tang W K S 2009 Chaos, Soliton. and Fract. 39 821
[7] Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成,刘中,许建平,朱雷 2010 物理学报 59 1540]
[8] Yu S, M, Lü J, Leung H, Chen G 2005 IEEE Trans. Circuits Syst. I, Reg. Papers 52 1459
[9] Celikovsky S, Chen G 2005 Chaos, Soliton. and Fract. 26 1271
[10] Deng B, Wang Z L, Hou C X, Yao F A 2010 J. Univ. Jinan (Sci. and Tech.) 24 402 (in Chinese) [邓斌,王忠林,侯承玺,姚福安 2010 济南大学学报(自然科学版) 24 402]
[11] Wang Z L, Huang N 2010 J. Ocean Univ China 40 131 (in Chinese) [王忠林,黄娜 2010 中国海洋大学学报 40 131]
[12] Grassi G 2008 Chin. Phys. B 17 3247
[13] Grassi G, Severance F L Miller D A 2009 Chaos, Soliton. and Fract. 41 284
[14] Wang Z, Qi G, Sun Y, vanWyk B J, vanWyk M A 2010 Nonlinear Dyn. 60 443
[15] 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]
[16] Jia H Y, Chen Z Z, Ye F 2011 Acta Phys. Sin. 60 203 (in Chinese) [贾红艳,陈增强,叶菲 2011 物理学报 60 203]
[17] Cang S, Qi G, Chen Z 2010 Nonlinear Dyn. 59 515
[18] Qi G, vanWyk B J, vanWyk M A 2009 Chaos, Soliton. and Fract. 40 2016
[19] Liu C, Liu T, Liu L, Liu K 2004 Chaos, Soliton. and Fract. 22 1031
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[1] 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]
[2] Li Q D, Yang X S Yang F Y 2003 Electron. Lett. 39 1306
[3] Lü J, Chen G, Yu X, Leung H 2004 IEEE Trans. Circuits Syst. I, Reg. Papers 51 2476
[4] Han F, Yu X, Wang Y, Feng Y Chen G 2003 Electron. Lett. 39 1636
[5] Lü J, Han F, Yu X, Chen G 2004 Automatica 40 1677
[6] Yu S, Tang W K S 2009 Chaos, Soliton. and Fract. 39 821
[7] Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成,刘中,许建平,朱雷 2010 物理学报 59 1540]
[8] Yu S, M, Lü J, Leung H, Chen G 2005 IEEE Trans. Circuits Syst. I, Reg. Papers 52 1459
[9] Celikovsky S, Chen G 2005 Chaos, Soliton. and Fract. 26 1271
[10] Deng B, Wang Z L, Hou C X, Yao F A 2010 J. Univ. Jinan (Sci. and Tech.) 24 402 (in Chinese) [邓斌,王忠林,侯承玺,姚福安 2010 济南大学学报(自然科学版) 24 402]
[11] Wang Z L, Huang N 2010 J. Ocean Univ China 40 131 (in Chinese) [王忠林,黄娜 2010 中国海洋大学学报 40 131]
[12] Grassi G 2008 Chin. Phys. B 17 3247
[13] Grassi G, Severance F L Miller D A 2009 Chaos, Soliton. and Fract. 41 284
[14] Wang Z, Qi G, Sun Y, vanWyk B J, vanWyk M A 2010 Nonlinear Dyn. 60 443
[15] 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]
[16] Jia H Y, Chen Z Z, Ye F 2011 Acta Phys. Sin. 60 203 (in Chinese) [贾红艳,陈增强,叶菲 2011 物理学报 60 203]
[17] Cang S, Qi G, Chen Z 2010 Nonlinear Dyn. 59 515
[18] Qi G, vanWyk B J, vanWyk M A 2009 Chaos, Soliton. and Fract. 40 2016
[19] Liu C, Liu T, Liu L, Liu K 2004 Chaos, Soliton. and Fract. 22 1031
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