A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 11 Issue 5
May  2024

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
S. He, K. Sun, and H. Wang, “Dynamics of the fractional-order Lorenz system based on Adomian decomposition method and its DSP implementation,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1298–1300, May 2024. doi: 10.1109/JAS.2016.7510133
Citation: S. He, K. Sun, and H. Wang, “Dynamics of the fractional-order Lorenz system based on Adomian decomposition method and its DSP implementation,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1298–1300, May 2024. doi: 10.1109/JAS.2016.7510133

Dynamics of the Fractional-Order Lorenz System Based on Adomian Decomposition Method and Its DSP Implementation

doi: 10.1109/JAS.2016.7510133
More Information
  • loading
  • [1]
    I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Phys. Rev. Lett., vol. 91, no. 3, p. 34101, 2003. doi: 10.1103/PhysRevLett.91.034101
    [2]
    I. Grigorenko and E. Grigorenko, “Erratum: Chaotic dynamics of the fractional Lorenz system [Phys. Rev. Lett. 91, 034101(2003)],” Phys. Rev. Lett, vol. 96, no. 19, p. 199902, 2006. doi: 10.1103/PhysRevLett.96.199902
    [3]
    H. Jia, Z. Chen, and W. Xue, “Analysis and circuit implementation for the fractional-order Lorenz system,” Acta Phys. Sin., vol. 62, no. 14, p. 140503, 2013. doi: 10.7498/aps.62.140503
    [4]
    A. Charef, H. Sun, Y. Tsao, et al., “Fractal system as represented by singularity function,” IEEE Trans. Auto. Cont., vol. 37, no. 9, pp. 1465–1470, 1992. doi: 10.1109/9.159595
    [5]
    M. Wang, G. Sun, and Y. Wei, “Limitations of frequency domain approximation in the calculation of fractional order chaotic systems,” J. Herbin,Initit. Tech., vol. 43, no. 5, pp. 8–12, 2011.
    [6]
    F. Sadiki, K. Rasimi, A. Ibraimi, et al., “Approaches developed to solve fractional differential equations,” J. EJENS-Eur. J. Eng. Nat. Sci., vol. 8, p. 83, 2023.
    [7]
    K. Sun, X. Wang, and J. C. Sprott, “Bifurcations and chaos in fractional-order simplified Lorenz system,” Inter. J. Bifur. Chaos, vol. 20, no. 4, pp. 1209–1219, 2010. doi: 10.1142/S0218127410026411
    [8]
    R. Li and W. Chen, “Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems,” Nonlinear Dyn., vol. 76, no. 1, pp. 785–795, 2014. doi: 10.1007/s11071-013-1169-0
    [9]
    S. He, K. Sun, and H. Wang, “Solving of fractional-order chaotic system based on Adomian decomposition algorithm and its complexity analyses,” Acta Phys. Sin., vol. 63, no. 3, p. 30502, 2014. doi: 10.7498/aps.63.030502
    [10]
    G. Adomian, “A review of the decomposition method and some recent results for nonlinear equations,” Math. Comp. Model., vol. 13, no. 7, pp. 17–43, 1990. doi: 10.1016/0895-7177(90)90125-7
    [11]
    D. Cafagna and G. Grassi, “Bifurcation and chaos in the fractionalorder Chen system via a time-domain approach,” Int. J. Bifur. Chaos, vol. 18, no. 7, pp. 1845–1863, 2008. doi: 10.1142/S0218127408021415
    [12]
    R. Caponetto and S. Fazzino, “An application of Adomian decomposition for analysis of fractional-order chaotic systems,” Inter. J. Bifur. Chaos, vol. 23, no. 3, p. 1350050, 2013. doi: 10.1142/S0218127413500508
    [13]
    H. Cao, R. Chu, and Y. Cui, “Complex dynamical characteristics of the fractional-order cellular neural network and its DSP implementation,” Fractal and Fractional, vol. 7, no. 8, p. 633, 2023. doi: 10.3390/fractalfract7080633
    [14]
    D. Peng, K. Sun, S. He, et al., “What is the lowest order of the fractional-order chaotic systems to behave chaotically?” Chaos,Soliton Fract., vol. 119, pp. 163–170, 2019. doi: 10.1016/j.chaos.2018.12.022
    [15]
    D. Matignon, “Stability results for fractional differential equations with applications to control processing,” Comp. Eng. Sys. Appl., pp. 963–968, 1997.
    [16]
    L. Li, H. Peng, Q. Luo, et al., “Problem and analysis of stability decidable theory for a class of fractional order nonlinear system,” Acta Phys. Sin., vol. 62, no. 2, p. 20502, 2013. doi: 10.7498/aps.62.020502
    [17]
    M. S. Tavazoei and M. Haeri, “A proof for non existence of periodic solutions in time invariant fractional order systems,” Automatica, vol. 45, no. 8, pp. 1886–1890, 2009. doi: 10.1016/j.automatica.2009.04.001

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

    Figures(7)

    Article Metrics

    Article views (115) PDF downloads(13) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return