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Design and implementation of an arbitrary poincare plane section circuit in three-dimensional space

Chen Hong Wu Ling

Design and implementation of an arbitrary poincare plane section circuit in three-dimensional space

Chen Hong, Wu Ling
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  • 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.
    • 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).
    [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 物理学报 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 物理学报 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 物理学报 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]

    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 物理学报 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 物理学报 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 物理学报 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] Zhang Shi, Wang Pan, Zhang Rui-Hao, Chen Hong. A new method for selecting arbitrary Poincare section. Acta Physica Sinica, 2020, 69(4): 040503. doi: 10.7498/aps.69.20191585
    [2] Wang Lin, Wei Lai, Wang Zheng-Xiong. Effect of out-of-plane driving flow on formation of plasmoids in current sheet system. Acta Physica Sinica, 2020, 69(5): 059401. doi: 10.7498/aps.69.20191612
    [3] Zhang Zhan-Gang, Lei Zhi-Feng, Tong Teng, Li Xiao-Hui, Wang Song-Lin, Liang Tian-Jiao, Xi Kai, Peng Chao, He Yu-Juan, Huang Yun, En Yun-Fei. Comparison of neutron induced single event upsets in 14 nm FinFET and 65 nm planar static random access memory devices. Acta Physica Sinica, 2020, 69(5): 056101. doi: 10.7498/aps.69.20191209
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  • Received Date:  13 February 2012
  • Accepted Date:  16 August 2012
  • Published Online:  20 January 2013

Design and implementation of an arbitrary poincare plane section circuit in three-dimensional space

  • 1. Electronic Engineer College, Heilongjiang University, Harbin 150080, China
Fund Project:  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).

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.

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