, 92:97 | Cite as

Parameter estimation of chaotic systems based on extreme value points

  • Zhihuan Chen
  • Xiaohui YuanEmail author
  • Xu Wang
  • Yanbin Yuan


Parameter estimation and synchronisation of chaotic systems are one of the hottest topics in the field of nonlinear science. In this paper, we addressed how to utilise the obtained experimental time series to estimate multiple parameters in chaotic systems. On the basis of relations of critical points and extreme value points, as well as the least squares estimation, we deduced a novel statistical parameter estimation corollary method to evaluate the unknown parameters in chaotic systems. In order to illustrate the feasibility and effectiveness of the proposed method, three numerical simulation results are presented, where the validity of the proposed method is verified in detail. Furthermore, we also investigated the effects of time-series noise and system disturbances for the proposed method, and the results showed that the proposed method is robust to uncertainties.


Parameter estimation chaotic system time series least squares estimation noise 


05.45.−a 05.40.Ca 



This work was supported by the National Natural Science Foundation of China (Nos 41571514, U1765201) and the Fundamental Research Funds for the Central Universities (No. 2017KFYXJJ204).


  1. 1.
    N Noghredani, A Riahi, N Pariz and A Karimpour, Pramana – J. Phys. 90: 26 (2018)ADSCrossRefGoogle Scholar
  2. 2.
    A Khan, D Khattar and N Prajapati, Pramana – J. Phys. 89: 90 (2017)ADSCrossRefGoogle Scholar
  3. 3.
    W Yu and J Cao, Physica A 375(2), 467 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    H Abarbanel, D Creveling and J Jeanne, Phys. Rev. E 77(1), 016208 (2008)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Y Xu, W Zhou and J Fang, Phys. Lett. A 374(34), 3441 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    X Gao and H Hu, Appl. Math. Modell. 39, 3980 (2015)CrossRefGoogle Scholar
  7. 7.
    J Liu and S Liu, Appl. Math. Modell. 48, 440 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    J Annan, D Lunt and J Hargreaves, Nonlinear Process. Geophys. 12(3), 363 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    H Peng, L Li and Y Yang, Chaos 19(3), 033130 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    V Pisarenko and D Sornette, Phys. Rev. E 69(3), 036122 (2004)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    J Lazzus, M Rivera and C Lopez-Caraballo, Phys. Lett. A 380(11), 1164 (2016)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Q Jiang, L Wang and X Hei, J. Comput. Sci. 8, 20 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    X Yuan, Z Chen, Y Yuan and Y Huang, Energy 93, 173 (2015)CrossRefGoogle Scholar
  14. 14.
    J Sun, J Zhao and X Wu, Phys. Lett. A 374(28), 2816 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    J Liang, X Yuan and Y Yuan, Mech. Syst. Sign. Process. 85, 927 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    W Li, C Meng and D Sheng, Challen. Power Engin. Environ. 1, 286 (2007)CrossRefGoogle Scholar
  17. 17.
    O Rossler, Phys. Lett. A 71(2–3), 155 (1979)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    E Lorenz, J. Atmos. Sci. 20(2), 130 (1963)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    L Alonso, Chaos 25(3), 033104 (2015)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Z Chen, X Yuan, B Ji, P Wang and H Tian, Energy Convers. Manage. 84, 390 (2014)CrossRefGoogle Scholar
  21. 21.
    A Sitz, U Schwarz and J Kurths, Phys. Rev. E 66(1), 016210 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    R Behinfaraz, M Badamchizadeh and A Ghiasi, Appl. Math. Modell. 40(7), 4468 (2016)CrossRefGoogle Scholar
  23. 23.
    Z Chen, X Yuan and Y Yuan, IEEE Trans. Circ. Syst. I: Regul. Pap. 63(9), 1464 (2016)Google Scholar
  24. 24.
    M Hu, Z Xu and R Zhang, Phys. Lett. A 361(3), 231 (2007)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    X Yuan, B Ji, Y Yuan, R M Ikram, X Zhang and Y Huang, Energy Convers. Manage. 91, 225 (2015)CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Hydropower and Information EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower StationChina Three Gorges UniversityYichangChina
  3. 3.State Key Laboratory of Simulation and Regulation of Water Cycle in River BasinChina Institute of Water Resources and Hydropower ResearchBeijingChina
  4. 4.School of Resource and Environmental EngineeringWuhan University of TechnologyWuhanChina

Personalised recommendations