WU Senlin, LI Yaotian, LI Wenshi, LI Lei. Chaos Criteria Design Based on Modified Sign Functions with One or Three-Threshold[J]. Chinese Journal of Electronics, 2019, 28(2): 364-369. doi: 10.1049/cje.2018.02.001
Citation: WU Senlin, LI Yaotian, LI Wenshi, LI Lei. Chaos Criteria Design Based on Modified Sign Functions with One or Three-Threshold[J]. Chinese Journal of Electronics, 2019, 28(2): 364-369. doi: 10.1049/cje.2018.02.001

Chaos Criteria Design Based on Modified Sign Functions with One or Three-Threshold

doi: 10.1049/cje.2018.02.001
Funds:  This work is supported by the Natural Science Foundation of Jiangsu Province of China (No.BK20141196), Technological Innovation of Key Industries in Suzhou City Prospective Application Study (No.SYG201701), and RIGOL University-Enterprise Cooperative Project of Ministry of Education (No.201702125008).
More Information
  • Corresponding author: LI Wenshi (corresponding author) was born in Harbin, Heilongjiang Province, China, in 1963. He received the B.S. degree in 1987 in physics from Harbin Normal University, and received the M.S. degree in electronics at Nanjing University in 1990. In 2009, he completed his microelectronics Ph.D. degree at Southeast University. He was a visiting scholar/researcher at Fudan University in 2001; at Tohoku University, Japan in 2007; and at Nanjing University in 2009. Prof. LI has worked at the Department of Microelectronics at Soochow University since 2001; He is working at the subnano scale with new synaptic circuit, to try and understand how brain circuitry works. (Email:lwshi@suda.edu.cn)
  • Received Date: 2017-10-22
  • Rev Recd Date: 2017-12-06
  • Publish Date: 2019-03-10
  • The complexity measures of chaotic or periodic signals are perpetual topics of interest to data scientists. This work adheres to the framework of the traditional 0-1 test for chaos and replaces sine and cosine functions by modified sign functions. The compressive mapping rules chosen are one-threshold of three-value or three-threshold of five-value. In new criteria for chaos in forms of the 3s plot and Ks metric compared with 0-1 test results, the periodic state of data features a short beeline instead of a big ring in the pq plot and signs the nearest zero mark, while the chaotic state signs a simple curve instead of a random-walking shape in the pq plot, and shows the nearest one mark. By computing the Lorenz equation evolution under the contrast tests of the Poincare section and Lyapunov index, we visualize a new chaoscriteria design in symbolic dynamics and data compression principles, and our work may lay the foundation for further expressing the chaotic appearance of novel signals deep into future brainets.
  • loading
  • A. Cangelosi and S. Invitto, “Human-robot interaction and neuroprosthetics: A review of new technologies”, IEEE Consumer Electronics Magazine, Vol.6, No.3, pp.24-33, 2017.
    T.S. Parker and L.O. Chua, “Chaos: A tutorial for engineers”, Proceedings of the IEEE, Vol.75, No.8, pp.982-108, 1987.
    T.Y. Li and J.A. Yorke, “Period three implies chaos”, The American Mathematical Monthly, Vol.82, No.10, pp.985-992, 1975.
    A.L. Robinson, “Physicists try to find order in chaos”, Science, Vol.218, No.4572, pp.554-556, 1982.
    L. Larger and J.M. Dudley, “Nonlinear dynamics: Optoelectronic chaos”, Nature, Vol.465, pp.41-42, 2010.
    N.H. Packard, J.P. Grutchfield, J.D. Farmer, et al., “Geometry from a time series”, Physical Review Letters, Vol.45, No.9, pp.712-716, 1980.
    J.P. Eckmann and D. Ruelle, “Ergodic theory of chaos and strange attractors”, Reviews of Modern Physics, Vol.57, No.3, pp.617-656, 1985.
    Wanda Szemplińka-Stupnicka, “The analytical predictive criteria for chaos and escape in nonlinear oscillators: A survey”, Nonlinear Dynamics, Vol.7, No.2, pp.129-147, 1995.
    H.D.I. Abarbanel, T.W. Frison and L.S. Tsimring, “Obtaining order in a world of chaos: Time-domain analysis of nonlinear and chaotic signals”, IEEE Signal Processing Magazine, Vol.15, No.3, pp.49-65, 1998.
    M. Sano and Y. Sawada, “Measurement of the Lyapunov spectrum from a chaotic time series”, Physical Review Letters, Vol.55, No.10, pp.1082-1085, 1985.
    V.K. Melnikov, “On the stability of the center for time periodic perturbations”, Transactions of the Moscow Mathematical Society, No.12, pp.1-57, 1963.
    Nie Chunyan, “A research of identifying chaotic nature based on chaos”, Journal of Chuangchun University, Vol.13, No.1, pp.13-15, 2003. (in Chinese)
    Zheng Boren, “Chaotic behavior’s decision and criterion of electronic systems”, Modern Electronic Technology, Vol.10, No.14, pp.157-159, 2007. (in Chinese)
    G.A. Gottwald and I. Melbourne, “A new test for chaos in deterministic systems”, Proceedings of the Royal Society A, Vol.460, pp.603-611, 2004.
    J. Hu, W.W. Tung, J. Gao, et al., “Reliability of the 0-1 test for chaos”, Physical Review E, Vol.72, No.5, pp.056207-1-5, 2005.
    G.A. Gottwald and I. Melbourne, “Comment on ‘Reliability of the 0-1 test for chaos’ ”, Physical Review E, Vol.77, No.2, pp.028201-1-3, 2008.
    G.A. Gottwald and I. Melbourne, “On the implementation of the 0-1 test for chaos”, SIAM Journal on Applied Dynamical Systems, Vol.8, No.1, pp.129-145, 2009.
    K.H. Sun, X. Liu and C.X. Zhu, “The 0-1 test algorithm for chaos and its applications”, Chinese Physics B, Vol.19, No.11, pp.110510-1-7, 2010.
    C.S. Kenney and A.J. Laub, “The matrix sign function”, IEEE Transactions on Automatic Control, Vol.40, No.8, pp.1330-1348, 1995.
    M. Lehrman and A.B. Rechester, “Symbolic analysis of chaotic signals and turbulent fluctuations”, Physical Review Letters, Vol.78, No.1, pp.54-57, 1997.
    A.K. Jain, “Image data compression: A review”, Proceedings of the IEEE, Vol.69, No.3, pp.349-389, 1981.
    Jin Tao and Bai Fengming, “The study on judgement of chaotic threshold for chaos-based detection system based on the crossover technique”, Journal of Changchun University of Science and Technology (Natural Science Edition), Vol.33, No.1, pp.67-69, 2010. (in Chinese)
    J.R. Piper and J.C. Sprott, “Simple autonomous chaotic circuits”, IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, Vol.57, No.9, pp.730-734, 2010.
    J.C. Sprott and S.J. Linz, “Algebraically simple chaotic flows”, International Journal of Chaos Theory and Applications, Vol.5, No.2, pp.1-20, 2000.
    J.M. Malasoma, “A new class of minimal chaotic flows”, Physics Letters A, Vol.305, No.1-2, pp.52-58, 2002.
    K.H. Sun and J.C. Sprott, “Dynamics of a simplified Lorenz system”, International Journal of Bifurcation and Chaos, Vol.19, No.4, pp.1357-1366, 2009.
    L.F. Shampine and M.W. Reichelt, “The MATLAB ode suite”, SIAM Journal on Scientific Computing, Vol.18, No.1, pp.1-22, 1997.
    N. Marwan, “A historical review of recurrence plots? European Physical Journal ST, Vol.164, No.1, pp.3-12, 2008.
    W.S. Li, L. Li and J.J. Song, “A basic chemical synaptic Euler model and its triad trigger topology”, Chinese Journal of Electronics, Vol.26, No.2, pp.244-249, 2017.
    W.S. Li, Micro-nano-electronics Modeling: Case Study, Soochow University Press, Suzhou, China, 2016. (in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (131) PDF downloads(142) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return