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A constructing approach to generating N×M-scroll attractors with polynomial and step function is reported. In Chuas circuit, only two or three scrolls can be generated by traditional polynomial function. On this basis, the multi-scroll of x direction in phase space is obtained by polynomial shift. And then the saddle-focus equilibrium points with index-2 in phase space are extended by combining both polynomial and step function, which makes it possible to extend the multi-scroll in y direction. Then the grid multi-scroll chaotic attractors are generated. The main feature of this constructing approach is generating grid multi-scroll chaotic attractors by combining both smooth curves and non-smooth curves for the first time. And the arbitrary planar grid multi-scroll chaotic attractors array can be generated by adjusting the values of natural numbers N and M. The effectiveness of this method has been verified by theoretical analysis, numerical simulation and circuit simulation.
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Keywords:
- grid multi-scroll chaotic attractors /
- Chuas circuit /
- step function /
- circuit implementation
[1] Deng W, Lü J H 2006 Chaos 16 043120
[2] Ahmad W M 2005 Chaos, Solitons Fractals 25 727
[3] Deng W 2007 Int. J. Bifurc. Chaos 17 3965
[4] Suyken J A K,Vandewalle J 1993 IEEE Trans. Circuits Syst.Ⅰ 40 861
[5] Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE International Symposium on Circuits and Systems Seattle, WA p768
[6] Zhang C X, Yu S M, Lü J H, Chen G R 2008 The 9th International Conference for Young Computer Scientists, Hunan p2840
[7] Yalcin M E 2007 Chaos, Solitons Fractals 34 1659
[8] Wang F G, Liu C X, Lu J J 2006 Acta Phys. Sin. 55 3289 (in Chinese) [王发强、刘崇新、逯俊杰 2006 物理学报 55 3289]
[9] Yu S M, Lin Q H, Qiu S S 2003 Acta Phys. Sin. 52 0025 (in Chinese) [禹思敏、林清华、丘水生 2003 物理学报 52 0025]
[10] Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707]
[11] Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 物理学报 56 1983]
[12] Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 (in Chinese) [谌 龙、彭海军、王德石 2008 物理学报 57 3337]
[13] Zhang C X, Yu S M 2009 Chin. Phys. B 18 0119
[14] Li R, Duan Z S, Wang B 2008 Int. J. Bifurc. Chaos 18 1865
[15] 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]
[16] Xu F, Yu P 2010 J. Math. Anal. Appl. 362 252
[17] Yalcin M E, Suykens J A K, Vandewall J 2002 Int. J. Bifurc. Chaos 12 23
[18] Lü J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst.Ⅰ 51 2476
[19] Lü J H, Han F, Yu X, Chen G R 2004 Automatica 40 1677
[20] Lü J H, Yu S M, Leung H, Chen G R 2005 Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS 05) Kobe, Japan p23
[21] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst.Ⅰ 53 149
[22] 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]
[23] Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 物理学报 54 1500]
[24] Yu S M, Tang W K S 2009 Chaos, Solitons Fractals 39 821
[25] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 0120 (in Chinese) [张朝霞、禹思敏 2009 物理学报 58 0120]
[26] Cafagna D, Grassi G2003 Int. J. Bifurc. Chaos 13 2537
[27] Cafagna D, Grassi G2003 Int. J. Bifurc. Chaos 13 2889
[28] Zhong G Q J 1994 IEEE Trans. Circuits Syst.Ⅰ 41 934
[29] Li Y, Yu S M, Dai Q Y, Liu M H, Liu Q 2006 Acta Phys. Sin. 55 3938 (in Chinese) [李 亚、禹思敏、戴青云、刘明华、刘 庆 2006 物理学报 55 3938]
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[1] Deng W, Lü J H 2006 Chaos 16 043120
[2] Ahmad W M 2005 Chaos, Solitons Fractals 25 727
[3] Deng W 2007 Int. J. Bifurc. Chaos 17 3965
[4] Suyken J A K,Vandewalle J 1993 IEEE Trans. Circuits Syst.Ⅰ 40 861
[5] Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE International Symposium on Circuits and Systems Seattle, WA p768
[6] Zhang C X, Yu S M, Lü J H, Chen G R 2008 The 9th International Conference for Young Computer Scientists, Hunan p2840
[7] Yalcin M E 2007 Chaos, Solitons Fractals 34 1659
[8] Wang F G, Liu C X, Lu J J 2006 Acta Phys. Sin. 55 3289 (in Chinese) [王发强、刘崇新、逯俊杰 2006 物理学报 55 3289]
[9] Yu S M, Lin Q H, Qiu S S 2003 Acta Phys. Sin. 52 0025 (in Chinese) [禹思敏、林清华、丘水生 2003 物理学报 52 0025]
[10] Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707]
[11] Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 物理学报 56 1983]
[12] Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 (in Chinese) [谌 龙、彭海军、王德石 2008 物理学报 57 3337]
[13] Zhang C X, Yu S M 2009 Chin. Phys. B 18 0119
[14] Li R, Duan Z S, Wang B 2008 Int. J. Bifurc. Chaos 18 1865
[15] 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]
[16] Xu F, Yu P 2010 J. Math. Anal. Appl. 362 252
[17] Yalcin M E, Suykens J A K, Vandewall J 2002 Int. J. Bifurc. Chaos 12 23
[18] Lü J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst.Ⅰ 51 2476
[19] Lü J H, Han F, Yu X, Chen G R 2004 Automatica 40 1677
[20] Lü J H, Yu S M, Leung H, Chen G R 2005 Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS 05) Kobe, Japan p23
[21] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst.Ⅰ 53 149
[22] 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]
[23] Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 物理学报 54 1500]
[24] Yu S M, Tang W K S 2009 Chaos, Solitons Fractals 39 821
[25] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 0120 (in Chinese) [张朝霞、禹思敏 2009 物理学报 58 0120]
[26] Cafagna D, Grassi G2003 Int. J. Bifurc. Chaos 13 2537
[27] Cafagna D, Grassi G2003 Int. J. Bifurc. Chaos 13 2889
[28] Zhong G Q J 1994 IEEE Trans. Circuits Syst.Ⅰ 41 934
[29] Li Y, Yu S M, Dai Q Y, Liu M H, Liu Q 2006 Acta Phys. Sin. 55 3938 (in Chinese) [李 亚、禹思敏、戴青云、刘明华、刘 庆 2006 物理学报 55 3938]
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