设计和实现三维空间任意庞加莱截平面电路

陈红; 吴玲

doi:10.7498/aps.62.020507

摘要

庞加莱截面法是简化分析复杂动力系统运动状态的有效方法. 为实现在线方便观测复杂系统的状态, 本文设计并实现了三维任意庞加莱截平面电子电路. 文章首先详细分析和研究了设计三维任意庞加莱截平面电路的关键性问题, 然后分类设计和实现了物理电路. 由于蔡氏电路具有丰富的动力学行为, 因此以典型的蔡氏电路作为实验待测动力系统, 对设计的截平面电路进行了大量的物理实验, 测出了蔡氏电路各种状态下的截平面图, 以及同一种混沌状态下选取不同截面的测试实验. 实验中采用了两种双踪示波器(模拟示波器和数字示波器)在线实测了庞加莱截平面映射和状态图. 与此同时, 利用Matlab进行了计算机仿真辅助实验. 所有实验结果表明设计的庞加莱截平面电路具有实用性和有效性.

关键词:

Abstract

The Poincare section method is an effective method to simplify the analysis of complex dynamic system motion state. To achieve online observing system states conveniently, an arbitrary directional Poincare plane section physical electronic circuit in three-dimensional space is designed and realized. Firstly, the key problems of an arbitrary Poincare plane section circuit design are analyzed and studied in detail. And then the physical circuit is realized in classification. As Chua's circuit has rich dynamic behaviors, the typical Chua's circuit is chosen as the experimental dynamical system. And then a lot of the physical experiments with this Poincare plane section circuit are performed in real time. For example, Poincare plane section diagrams in different conditions of Chua's circuit are measured, and the test experiments in the same kind of chaotic state, with different plane sections chosen, are carried out. All Poincare section map diagrams and phase diagrams are measured by two double-channel oscilloscopes (analogue oscilloscope and digital oscilloscope). At the same time, computer simulation experiments are conducted by using Matlab. These results show the practicability and effectiveness of the Poincare plane section circuit.

Keywords:

作者及机构信息

陈红,
吴玲

1.
黑龙江大学电子工程学院, 哈尔滨 150080

基金项目: 国家自然科学基金(批准号: 61072072)、黑龙江省自然科学基金(批准号: F201249)、黑龙江省教育厅科研项目(批准号: 12521402) 和黑龙江省普通高等学校电子工程重点实验室(批准号: DZZD20100021)资助的课题.

Authors and contacts

Chen Hong,
Wu Ling

1.
Electronic Engineer College, Heilongjiang University, Harbin 150080, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61072072), the Nature Science Foundation of Heilongjiang Province (Grant No. F201249), the Scientific Research Foundation of the Education Department of Heilongjiang Province China (Grant No. 12521402), and Key Laboratory of Electronics Engineering, College of Heilongjiang Province, China (Grant No. DZZD20100021).

参考文献

[1]	Ma Y, Gu M L 2006 Audio Engineering 8 39 (in Chinese) [马勇, 顾明亮 2006 电声技术 8 39]
[2]	Li P, Shen D, Jia X N 2011 J. Clin Anesthesiol. 27 116 (in Chinese) [李佩, 申岱, 贾晓宁 2011 临床麻醉学 27 116]
[3]	Zhao J J, Zhang Y 2008 Adv. Cardiovasc Dis. 29 91 (in Chinese) [赵进军, 张颖 2008 心血管病学进展 29 91]
[4]	Strumillo P, Ruta J 2002 IEEE Engineering in Medicine and Biology 21 62
[5]	Zhou G H, Xu J P, Bao B C, Wang J P, Jin Y Y 2011 Acta Phys. Sin. 60 010503 (in Chinese) [周国华, 许建平, 包伯城, 王金平, 金艳艳 2011 60 010503]
[6]	Pan C, Zhang J M 2007 Journal of spacecraft TT&C Technology 26 76 (in Chinese) [潘昶, 张建民 2007 飞行器测控学报 26 76]
[7]	Zhang H Q, Li Y J 2011 The 3rd IEEE International Conference on Advanced Computer Control Harbin, China, January 18-20, 2011 p417 (IEEE)
[8]	Chen H, Gao M Z 2010 The Third International Workshop on Chaos-Fractals Theories and Applications Kunming, China, October 29-31, 2010 p221 (IEEE)
[9]	Wu X Z, LI Z X, Zhang Y X, Feng R F, Gu J Z, Zhuo Y Z 2001 Science in China (Series A) 44 923
[10]	Zhou X Y 2011 Acta Phys. Sin. 60 100503 (in Chinese) [周小勇 2011 60 100503]
[11]	Chen D Y, Shen T, Ma X Y 2011 Acta Phys. Sin. 60 050505 (in Chinese) [陈帝伊, 申滔, 马孝义 2011 60 050505]
[12]	Peng S J, Shui H T, Ma H X 2011 Control Engineering of China 18 142 (in Chinese) [彭胜军, 税海涛, 马宏绪 2011 控制工程 18 142]
[13]	Zhang J, Hui M 2011 Journal of Circuits and Systems 16 80 (in Chinese) [张皎, 惠萌 2011 电路与系统学报 16 80]
[14]	Wang L, Peng J H, Zhang L J 2007 Journal of Shenzhen University Science and Engineering 24 290 (in Chinese) [王琳, 彭建华, 张立静 2007 深圳大学学报理工版 24 290]
[15]	Chai Wah Wu, Rulkov N F 1993 IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 40 707
[16]	Matsumoto T, Chua L O, Komuro M 1985 IEEE Transactions on Circuits and Systerms CAS-32 797

施引文献

[1]	Ma Y, Gu M L 2006 Audio Engineering 8 39 (in Chinese) [马勇, 顾明亮 2006 电声技术 8 39]
[2]	Li P, Shen D, Jia X N 2011 J. Clin Anesthesiol. 27 116 (in Chinese) [李佩, 申岱, 贾晓宁 2011 临床麻醉学 27 116]
[3]	Zhao J J, Zhang Y 2008 Adv. Cardiovasc Dis. 29 91 (in Chinese) [赵进军, 张颖 2008 心血管病学进展 29 91]
[4]	Strumillo P, Ruta J 2002 IEEE Engineering in Medicine and Biology 21 62
[5]	Zhou G H, Xu J P, Bao B C, Wang J P, Jin Y Y 2011 Acta Phys. Sin. 60 010503 (in Chinese) [周国华, 许建平, 包伯城, 王金平, 金艳艳 2011 60 010503]
[6]	Pan C, Zhang J M 2007 Journal of spacecraft TT&C Technology 26 76 (in Chinese) [潘昶, 张建民 2007 飞行器测控学报 26 76]
[7]	Zhang H Q, Li Y J 2011 The 3rd IEEE International Conference on Advanced Computer Control Harbin, China, January 18-20, 2011 p417 (IEEE)
[8]	Chen H, Gao M Z 2010 The Third International Workshop on Chaos-Fractals Theories and Applications Kunming, China, October 29-31, 2010 p221 (IEEE)
[9]	Wu X Z, LI Z X, Zhang Y X, Feng R F, Gu J Z, Zhuo Y Z 2001 Science in China (Series A) 44 923
[10]	Zhou X Y 2011 Acta Phys. Sin. 60 100503 (in Chinese) [周小勇 2011 60 100503]
[11]	Chen D Y, Shen T, Ma X Y 2011 Acta Phys. Sin. 60 050505 (in Chinese) [陈帝伊, 申滔, 马孝义 2011 60 050505]
[12]	Peng S J, Shui H T, Ma H X 2011 Control Engineering of China 18 142 (in Chinese) [彭胜军, 税海涛, 马宏绪 2011 控制工程 18 142]
[13]	Zhang J, Hui M 2011 Journal of Circuits and Systems 16 80 (in Chinese) [张皎, 惠萌 2011 电路与系统学报 16 80]
[14]	Wang L, Peng J H, Zhang L J 2007 Journal of Shenzhen University Science and Engineering 24 290 (in Chinese) [王琳, 彭建华, 张立静 2007 深圳大学学报理工版 24 290]
[15]	Chai Wah Wu, Rulkov N F 1993 IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 40 707
[16]	Matsumoto T, Chua L O, Komuro M 1985 IEEE Transactions on Circuits and Systerms CAS-32 797

[1]	郭慧朦, 梁燕, 董玉姣, 王光义. 蔡氏结型忆阻器的简化及其神经元电路的硬件实现. , 2023, 72(7): 070501. doi: 10.7498/aps.72.20222013
[2]	张识, 王攀, 张瑞浩, 陈红. 选取任意庞加莱截面的新方法. , 2020, 69(4): 040503. doi: 10.7498/aps.69.20191585
[3]	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
[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]	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
[6]	张晓芳, 陈小可, 毕勤胜. 多分界面下四维蔡氏电路的张弛簇发及其机制研究. , 2013, 62(1): 010502. doi: 10.7498/aps.62.010502
[7]	季颖, 毕勤胜. 高维广义蔡氏电路中的快慢动力学行为及其分岔分析. , 2012, 61(1): 010202. doi: 10.7498/aps.61.010202
[8]	余跃, 张春, 韩修静, 毕勤胜. 两子系统在周期切换连接下的振荡行为及其机理. , 2012, 61(20): 200507. doi: 10.7498/aps.61.200507
[9]	马文聪, 金宁德, 高忠科. 动力学变换法探测连续系统不稳定周期轨道. , 2012, 61(17): 170510. doi: 10.7498/aps.61.170510
[10]	陈仕必, 曾以成, 徐茂林, 陈家胜. 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. , 2011, 60(2): 020507. doi: 10.7498/aps.60.020507
[11]	冯朝文, 蔡理, 张立森, 杨晓阔, 赵晓辉. SETMOS实现多涡卷蔡氏电路的研究. , 2010, 59(12): 8426-8431. doi: 10.7498/aps.59.8426
[12]	冯朝文, 蔡理, 张立森, 杨晓阔, 赵晓辉. SETMOS在蔡氏电路中的特性研究. , 2010, 59(12): 8420-8425. doi: 10.7498/aps.59.8420
[13]	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
[14]	李亚, 张正明, 陶志杰. 一个超混沌六阶蔡氏电路及其硬件实现. , 2009, 58(10): 6818-6822. doi: 10.7498/aps.58.6818
[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]	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
[17]	李建芬, 李农, 林辉. 适合传输快变信息信号的混沌调制保密通信. , 2004, 53(6): 1694-1698. doi: 10.7498/aps.53.1694
[18]	刘崇新. 蔡氏对偶混沌电路分析. , 2002, 51(6): 1198-1202. doi: 10.7498/aps.51.1198
[19]	罗晓曙, 汪秉宏, 陈关荣, 蒋品群, 方锦清, 全宏俊. 混沌系统的参数开关调制法研究. , 2002, 51(5): 988-993. doi: 10.7498/aps.51.988
[20]	王震宇, 廖红印, 周世平. 直流偏置的与RLC谐振器耦合的约瑟夫森结动力学行为的数值模拟. , 2001, 50(10): 1996-2000. doi: 10.7498/aps.50.1996

计量

文章访问数: 6869
PDF下载量: 863
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