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).

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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

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