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In this paper, a new three-dimensional autonomous chaotic system is proposed. However, the structural form of the new chaotic system is limited to a double-wing like most Lorenz-like systems. According to the equilibrium points and topological structure of this double-wing chaotic system we design some appropriate nonlinear functions for it. Then, the new double-wing chaotic system can be modified into a grid multi-wing chaotic system. Basic dynamical properties of the system are studied by theoretical analysis and numerical simulation, which proves the chaotic behaviors of this new grid multi-wing chaotic system. Finally, an oscillator circuit is designed for implementation. The circuit simulation results are in good agreement with the numerical simulation results.
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Keywords:
- new three-dimensional chaotic system /
- equilibrium points /
- nonlinear functions /
- grid multi-wing chaotic attractors
[1] Chien T, Liao T L 2005 Chaos Soliton. Fract. 24 241
[2] Li R H, Xu W, Li S 2007 Chin. Phys. B 16 1591
[3] Niu Y D, Ma W Q, Wang R 2009 Acta Phys. Sin. 58 2934 (in Chinese) [牛永迪, 马文强, 王荣 2009 物理学报 58 2934]
[4] Liu Y R, Wu Z M, Wu J G, Li P, Xia G Q 2012 Acta Phys. Sin. 61 024203 (in Chinese) [刘宇然, 吴正冒, 吴加贵, 李萍, 夏光琼 2012 物理学报 61 024230]
[5] Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[6] Bao B C, Zhu L, Wang X F, Zhong L, Xu J P 2010 International Conference on Communications, Circuit and Systems (ICCCAS) Changchun, China, July 28-30, 2010 p747
[7] Chen S B, Zeng Y C, Xu M L, Chen J S 2011 Acta Phys. Sin. 60 020507 (in Chinese) [陈仕必, 曾以诚, 徐茂林, 陈家胜 2011 物理学报 60 020507]
[8] 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]
[9] Dadras S, Momeni H R 2009 Phys. Lett. A 373 3637
[10] Chen Y, Yang Y Q 2010 Chin. Phys. B 19 120510
[11] Chen Z Q, Yang Y, Yuan Z Z 2008 Chaos Soliton. Fract. 38 1187
[12] Liu X Y 2009 Chin. Phys. Lett. 26 0504
[13] 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, 陈曾强, 袁著祗 2007 物理学报 56 3137]
[14] Hu S G 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡四国 2009 物理学报 58 3743]
[15] Yu F, Wang C H, Yin J W, Xu H 2012 Acta Phys. Sin. 61 020506 (in Chinese) [余飞, 王春华, 尹晋文, 徐浩 2012 物理学报 61 020506]
[16] Zhang C X, Yu S M, Lü J H, Chen G R 2008 The 9th International Conference for Yong Computer Scientists Hunan, China, November 18-21, 2008 p2804
[17] Bao B C, Wang X F, Xu J P 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA) Kunming, China, October 29-31, 2010 p211
[18] Yu S M, Lü J H, Tang W K S, Chen G R 2008 IEEE International Symposium on Circuits and Systems Seattle, USA, May 18-21, 2008 p768
[19] Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168
[20] Yu S M, Lü J H, Chen G R, Yu X H 2010 IEEE Trans. Circuits Syst. II 57 803
[21] Qi G Y, Wyk B J, Wyk M A 2007 Chaos Soliton. Fract. 40 2016
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[1] Chien T, Liao T L 2005 Chaos Soliton. Fract. 24 241
[2] Li R H, Xu W, Li S 2007 Chin. Phys. B 16 1591
[3] Niu Y D, Ma W Q, Wang R 2009 Acta Phys. Sin. 58 2934 (in Chinese) [牛永迪, 马文强, 王荣 2009 物理学报 58 2934]
[4] Liu Y R, Wu Z M, Wu J G, Li P, Xia G Q 2012 Acta Phys. Sin. 61 024203 (in Chinese) [刘宇然, 吴正冒, 吴加贵, 李萍, 夏光琼 2012 物理学报 61 024230]
[5] Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[6] Bao B C, Zhu L, Wang X F, Zhong L, Xu J P 2010 International Conference on Communications, Circuit and Systems (ICCCAS) Changchun, China, July 28-30, 2010 p747
[7] Chen S B, Zeng Y C, Xu M L, Chen J S 2011 Acta Phys. Sin. 60 020507 (in Chinese) [陈仕必, 曾以诚, 徐茂林, 陈家胜 2011 物理学报 60 020507]
[8] 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]
[9] Dadras S, Momeni H R 2009 Phys. Lett. A 373 3637
[10] Chen Y, Yang Y Q 2010 Chin. Phys. B 19 120510
[11] Chen Z Q, Yang Y, Yuan Z Z 2008 Chaos Soliton. Fract. 38 1187
[12] Liu X Y 2009 Chin. Phys. Lett. 26 0504
[13] 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, 陈曾强, 袁著祗 2007 物理学报 56 3137]
[14] Hu S G 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡四国 2009 物理学报 58 3743]
[15] Yu F, Wang C H, Yin J W, Xu H 2012 Acta Phys. Sin. 61 020506 (in Chinese) [余飞, 王春华, 尹晋文, 徐浩 2012 物理学报 61 020506]
[16] Zhang C X, Yu S M, Lü J H, Chen G R 2008 The 9th International Conference for Yong Computer Scientists Hunan, China, November 18-21, 2008 p2804
[17] Bao B C, Wang X F, Xu J P 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA) Kunming, China, October 29-31, 2010 p211
[18] Yu S M, Lü J H, Tang W K S, Chen G R 2008 IEEE International Symposium on Circuits and Systems Seattle, USA, May 18-21, 2008 p768
[19] Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168
[20] Yu S M, Lü J H, Chen G R, Yu X H 2010 IEEE Trans. Circuits Syst. II 57 803
[21] Qi G Y, Wyk B J, Wyk M A 2007 Chaos Soliton. Fract. 40 2016
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