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A new method to generate multi-wing butterfly chaotic attractors is presented. Based on the three-dimensional Lorenz system, in this paper we propose a four-dimensional multi-wing chaotic system by appending a state variable and a piecewise linear function. The equilibrium points and Lyapunov exponent spectra 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 /
- Lorenz system /
- four-dimensional multi-wing chaotic system /
- circuit implementation
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chen G, Ueta T 1999 Int. J. Bifurcation and Chaos 9 1465
[3] L J H, Chen G R 2002 Int. J. Bifurcation and Chaos 12 659
[4] L J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifurcation and Chaos 12 2917
[5] Liu W B, Chen G R 2003 Int. J. Bifurcation and Chaos 13 261
[6] Liu W B, Chen G R 2004 Int. J. Bifurcation and Chaos 14 1395
[7] Qi G Y, Chen G R, Li S W, Zhang Y H 2006 Int. J. Bifurcation and Chaos 16 859
[8] 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 56 3137]
[9] Chen Z Q, Yang Y, Yuan Z Z 2008 Chaos, Solitons & Fractals 38 1187
[10] Giuseppe G 2008 Chin. Phys. B 17 3247
[11] Li D Q 2008 Phys. Lett. A 372 387
[12] Wang L 2009 Nonlinear Dyn. 56 453
[13] Dong E Z, Chen Z P, Chen Z Q, Yuan Z Z 2009 Chin. Phys. B 18 2680
[14] Dadras S, Momeni H R 2009 Phys. Lett. A 373 3637
[15] Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 58 3734]
[16] Qiao X H, Bao B C 2009 Acta Phys. Sin. 58 8152 (in Chinese) [乔晓华, 包伯成 2009 58 8152]
[17] Hu G S, Yu B 2009 Int. J. Mod. Phys. C 20 323
[18] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[19] Yu S M, L J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[20] Bouallegue K, Chaari A, Toumi A 2011 Chaos, Solitons & Fractals 44 79
[21] Yu S M, L J H, Chen G R, Yu X H 2011 IEEE Trans. Circuits Syst. II, Exp. Briefs 58 314
[22] Yu B, Hu G S 2010 Int. J. Bifurcation and Chaos 20 727
[23] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 58 8139]
[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] Yu S M, Tang W K S, L J H, Chen G R 2010 Int. J. Bifurcation and Chaos 20 29
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chen G, Ueta T 1999 Int. J. Bifurcation and Chaos 9 1465
[3] L J H, Chen G R 2002 Int. J. Bifurcation and Chaos 12 659
[4] L J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifurcation and Chaos 12 2917
[5] Liu W B, Chen G R 2003 Int. J. Bifurcation and Chaos 13 261
[6] Liu W B, Chen G R 2004 Int. J. Bifurcation and Chaos 14 1395
[7] Qi G Y, Chen G R, Li S W, Zhang Y H 2006 Int. J. Bifurcation and Chaos 16 859
[8] 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 56 3137]
[9] Chen Z Q, Yang Y, Yuan Z Z 2008 Chaos, Solitons & Fractals 38 1187
[10] Giuseppe G 2008 Chin. Phys. B 17 3247
[11] Li D Q 2008 Phys. Lett. A 372 387
[12] Wang L 2009 Nonlinear Dyn. 56 453
[13] Dong E Z, Chen Z P, Chen Z Q, Yuan Z Z 2009 Chin. Phys. B 18 2680
[14] Dadras S, Momeni H R 2009 Phys. Lett. A 373 3637
[15] Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 58 3734]
[16] Qiao X H, Bao B C 2009 Acta Phys. Sin. 58 8152 (in Chinese) [乔晓华, 包伯成 2009 58 8152]
[17] Hu G S, Yu B 2009 Int. J. Mod. Phys. C 20 323
[18] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[19] Yu S M, L J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[20] Bouallegue K, Chaari A, Toumi A 2011 Chaos, Solitons & Fractals 44 79
[21] Yu S M, L J H, Chen G R, Yu X H 2011 IEEE Trans. Circuits Syst. II, Exp. Briefs 58 314
[22] Yu B, Hu G S 2010 Int. J. Bifurcation and Chaos 20 727
[23] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 58 8139]
[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] Yu S M, Tang W K S, L J H, Chen G R 2010 Int. J. Bifurcation and Chaos 20 29
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