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A novel method is presented generating multi-wing butterfly chaotic attractors in this paper. Based on Liu chaotic system, a multi-wing butterfly chaotic system is constructed via designing a new piecewise linear function. The equilibrium point, Lyapunov exponent spectra, bifurcation diagram, phase diagram, frequency spectrum and Poincaré mapping of the system are studied. Furthermore, an electronic circuit is designed to implement the system. The experimental results are in agreement with numerical simulation results, which verify the feasibility and availability of this method.
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Keywords:
- chaos /
- Liu chaotic system /
- multi-wing butterfly attractors /
- circuit implementation
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[3] Liu W B, Chen G R 2004 Int. J. Bifur. Chaos 14 1395
[4] 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, 袁著址 2007 物理学报 56 3137]
[5] Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 物理学报 58 3734]
[6] Dong E Z, Chen Z P, Chen Z Q, Yuan Z Z 2009 Chin. Phys. B 18 2680
[7] Dadras S, Momeni H R 2009 Phys. Lett. A 373 3637
[8] Wang L 2009 Nonlinear Dyn. 56 453
[9] Giuseppe G 2008 Chin. Phys. B 17 3247
[10] Li D Q 2008 Phys. Lett. A 372 387
[11] Chen Z Q, Yang Y, Yuan Z Z 2008 Chaos Soliton. Fract. 38 1187
[12] 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]
[13] Hu G S, Yu B 2009 Int. J. Mod. Phys. C 20 323
[14] Huang Y, Zhang P, Zhao W F 2013 J. Southwest Univ. (Nat. Sci. Ed.) 35 127 (in Chinese) [黄沄, 张鹏, 赵卫峰 2013 西南大学学报 (自然科学版) 35 127]
[15] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[16] Yu S M, L J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[17] Bouallegue K, Chaari A, Toumi A 2011 Chaos Soliton. Fract. 44 79
[18] Yu B, Hu G S 2010 Int. J. Bifur. Chaos 20 727
[19] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 物理学报 58 8139]
[20] Yu S M, L J H, Chen G R, Yu X H 2011 IEEE Trans. Circuits Syst. II Exp. Briefs 58 314
[21] Yu S M, L J H, Yu X H, Chen G R 2012 IEEE Trans. Circuits Syst. I Reg. Papers 59 1015
[22] Elwakil A S, Özoğuz S, Kennedy M P 2002 IEEE Trans. Circuits Syst. I Reg. Papers 49 527
[23] Yu S M, Tang W K S, L J H, Chen G R 2010 Int. J. Bifur. Chaos 20 29
[24] Yu S M, Tang W K S, L J H, Chen G R 2008 IEEE Trans. Circuits Syst. II Exp. Briefs 55 1168
[25] Luo M W, Luo X H, Li H Q 2013 Acta Phys. Sin. 62 020512 (in Chinese) [罗明伟, 罗小华, 李华青 2013 物理学报 62 020512]
[26] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5061 (in Chinese) [王发强, 刘崇新 2006 物理学报 55 5061]
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[3] Liu W B, Chen G R 2004 Int. J. Bifur. Chaos 14 1395
[4] 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, 袁著址 2007 物理学报 56 3137]
[5] Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 物理学报 58 3734]
[6] Dong E Z, Chen Z P, Chen Z Q, Yuan Z Z 2009 Chin. Phys. B 18 2680
[7] Dadras S, Momeni H R 2009 Phys. Lett. A 373 3637
[8] Wang L 2009 Nonlinear Dyn. 56 453
[9] Giuseppe G 2008 Chin. Phys. B 17 3247
[10] Li D Q 2008 Phys. Lett. A 372 387
[11] Chen Z Q, Yang Y, Yuan Z Z 2008 Chaos Soliton. Fract. 38 1187
[12] 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]
[13] Hu G S, Yu B 2009 Int. J. Mod. Phys. C 20 323
[14] Huang Y, Zhang P, Zhao W F 2013 J. Southwest Univ. (Nat. Sci. Ed.) 35 127 (in Chinese) [黄沄, 张鹏, 赵卫峰 2013 西南大学学报 (自然科学版) 35 127]
[15] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[16] Yu S M, L J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[17] Bouallegue K, Chaari A, Toumi A 2011 Chaos Soliton. Fract. 44 79
[18] Yu B, Hu G S 2010 Int. J. Bifur. Chaos 20 727
[19] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 物理学报 58 8139]
[20] Yu S M, L J H, Chen G R, Yu X H 2011 IEEE Trans. Circuits Syst. II Exp. Briefs 58 314
[21] Yu S M, L J H, Yu X H, Chen G R 2012 IEEE Trans. Circuits Syst. I Reg. Papers 59 1015
[22] Elwakil A S, Özoğuz S, Kennedy M P 2002 IEEE Trans. Circuits Syst. I Reg. Papers 49 527
[23] Yu S M, Tang W K S, L J H, Chen G R 2010 Int. J. Bifur. Chaos 20 29
[24] Yu S M, Tang W K S, L J H, Chen G R 2008 IEEE Trans. Circuits Syst. II Exp. Briefs 55 1168
[25] Luo M W, Luo X H, Li H Q 2013 Acta Phys. Sin. 62 020512 (in Chinese) [罗明伟, 罗小华, 李华青 2013 物理学报 62 020512]
[26] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5061 (in Chinese) [王发强, 刘崇新 2006 物理学报 55 5061]
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