用多项式和阶跃函数构造网格多涡卷混沌吸引子及其电路实现

陈仕必; 曾以成; 徐茂林; 陈家胜

doi:10.7498/aps.60.020507

摘要

提出一种利用多项式和阶跃函数构造N×M涡卷的构造方法.利用蔡氏电路,传统的利用多项式函数只能产生双涡卷、三涡卷,在此基础上,通过多项式平移得到相空间x方向的多涡卷,再通过多项式与阶跃函数组合来扩展相空间中指标2的鞍焦平衡点,使得多涡卷向y方向延伸,从而生成网格多涡卷混沌吸引子.该构造方法的主要特征是通过光滑曲线和非光滑曲线的组合生成网格多涡卷混沌吸引子,能通过调整自然数N和M的值实现平面网格任意涡卷混沌吸引子阵列.理论分析、数值模拟和电路仿真证实了方法的可行性.

关键词:

Abstract

A constructing approach to generating N×M-scroll attractors with polynomial and step function is reported. In Chuas 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.

Keywords:

作者及机构信息

(1)北京信息科技大学,北京 100101; (2)湘潭大学材料与光电物理学院,湘潭 411105

基金项目: 国家自然科学基金(批准号:60972147)和湖南省自然科学基金(批准号:08JJ5031)资助的课题.

Authors and contacts

(1)Beijing Information Technology Institute, Beijing 100101, China; (2)School of Material Science and Photoelectronic Physics, Xiangtan University, Xiangtan 411105, China

参考文献

[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 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 52 0025]
[10]	Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 55 5707]
[11]	Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 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 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 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 59 1540]
[23]	Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 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 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 55 3938]

施引文献

[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 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 52 0025]
[10]	Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 55 5707]
[11]	Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 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 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 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 59 1540]
[23]	Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 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 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 55 3938]

[1]	林毅, 刘文波, 沈骞. 五阶压控忆阻蔡氏混沌电路的双稳定性. , 2018, 67(23): 230502. doi: 10.7498/aps.67.20181283
[2]	黄沄. 一类多翼蝴蝶混沌吸引子及其电路实现. , 2014, 63(8): 080505. doi: 10.7498/aps.63.080505
[3]	张新国, 孙洪涛, 赵金兰, 刘冀钊, 马义德, 韩廷武. 蔡氏电路的功能全同电路与拓扑等效电路及其设计方法. , 2014, 63(20): 200503. doi: 10.7498/aps.63.200503
[4]	马美玲, 闵富红, 邵书义, 黄苗玉. 基于符号函数的注入反馈式蔡氏电路同步控制. , 2014, 63(1): 010507. doi: 10.7498/aps.63.010507
[5]	左婷, 孙克辉, 艾星星, 王会海. 基于同相第二代电流传输器的网格多涡卷混沌电路研究. , 2014, 63(8): 080501. doi: 10.7498/aps.63.080501
[6]	吴先明, 何怡刚, 于文新. 基于电流反馈放大器的网格多涡卷混沌电路设计与实现. , 2014, 63(18): 180506. doi: 10.7498/aps.63.180506
[7]	罗明伟, 罗小华, 李华青. 一类四维多翼混沌系统及其电路实现. , 2013, 62(2): 020512. doi: 10.7498/aps.62.020512
[8]	王春华, 尹晋文, 林愿. 基于电流传输器的网格多涡卷混沌电路设计与实现. , 2012, 61(21): 210507. doi: 10.7498/aps.61.210507
[9]	武花干, 包伯成, 刘中. 吸引子涡卷数量与分布的控制:系统设计及电路实现. , 2011, 60(9): 090502. doi: 10.7498/aps.60.090502
[10]	杨志民, 张洁, 马永杰, 摆玉龙, 马胜前. 基于电流传输器的蔡氏混沌电路的设计和实现. , 2010, 59(5): 3007-3016. doi: 10.7498/aps.59.3007
[11]	薛薇, 郭彦岭, 陈增强. 永磁同步电机的混沌分析及其电路实现. , 2009, 58(12): 8146-8151. doi: 10.7498/aps.58.8146
[12]	张朝霞, 禹思敏. 用时滞和阶跃序列组合生成网格多涡卷蔡氏混沌吸引子. , 2009, 58(1): 120-130. doi: 10.7498/aps.58.120
[13]	仓诗建, 陈增强, 袁著祉. 一个新四维非自治超混沌系统的分析与电路实现. , 2008, 57(3): 1493-1501. doi: 10.7498/aps.57.1493
[14]	刘扬正. 超混沌Lü系统的电路实现. , 2008, 57(3): 1439-1443. doi: 10.7498/aps.57.1439
[15]	冯朝文, 蔡理, 康强. 基于单电子器件的混沌电路研究. , 2008, 57(10): 6155-6161. doi: 10.7498/aps.57.6155
[16]	王繁珍, 齐国元, 陈增强, 张宇辉, 袁著祉. 一个新的三维混沌系统的分析、电路实现及同步. , 2006, 55(8): 4005-4012. doi: 10.7498/aps.55.4005
[17]	张宇辉, 齐国元, 刘文良, 阎彦. 一个新的四维混沌系统理论分析与电路实现. , 2006, 55(7): 3307-3314. doi: 10.7498/aps.55.3307
[18]	王光义, 丘水生, 许志益. 一个新的三维二次混沌系统及其电路实现. , 2006, 55(7): 3295-3301. doi: 10.7498/aps.55.3295
[19]	李亚, 禹思敏, 戴青云, 刘明华, 刘庆. 一种新的蔡氏电路设计方法与硬件实现. , 2006, 55(8): 3938-3944. doi: 10.7498/aps.55.3938
[20]	李世华, 蔡海兴. Chen氏混沌电路实现与同步控制实验研究. , 2004, 53(6): 1687-1693. doi: 10.7498/aps.53.1687

计量

文章访问数: 9700
PDF下载量: 1217
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板