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提出了一个新的三维二次自治混沌系统, 与大多数广义Lorenz系统一样,该系统只能产生双翅膀吸引子. 依据该双翅膀混沌系统平衡点和吸引子的拓扑结构, 设计合适的非线性函数可以将其改进为一个产生网格多翅膀吸引子的混沌系统. 对该网格多翅膀混沌系统的基本动力学特性进行了分析, 证实了多翅膀吸引子的混沌特性. 最后设计了混沌电路, 给出了多翅膀混沌吸引子的电路仿真结果, 证实了理论设计与电路实现的一致性.
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关键词:
- 新三维二次自治混沌系统 /
- 平衡点 /
- 非线性函数 /
- 网格多翅膀混沌吸引子
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.-
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 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 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 60 020507]
[8] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞, 禹思敏 2009 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 56 3137]
[14] Hu S G 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡四国 2009 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 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 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 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 60 020507]
[8] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞, 禹思敏 2009 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 56 3137]
[14] Hu S G 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡四国 2009 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 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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