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Differential evolution algorithm-based parameter estimation for chaotic systems

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  • Peng, Bo
  • Liu, Bo
  • Zhang, Fu-Yi
  • Wang, Ling

Abstract

Parameter estimation for chaotic systems is an important issue in nonlinear science and has attracted increasing interests from various research fields, which could be essentially formulated as a multidimensional optimization problem. As a novel evolutionary computation technique, differential evolution algorithm (DE) has attracted much attention and wide applications, owing to its simple concept, easy implementation and quick convergence. However, to the best of our knowledge, there is no published work on DE for estimating parameters of chaotic systems. In this paper, a DE approach is applied to estimate the parameters of Lorenz system. Numerical simulation and the comparisons demonstrate the effectiveness and robustness of DE. Moreover, the effect of population size on the optimization performances is investigated as well.

Suggested Citation

  • Peng, Bo & Liu, Bo & Zhang, Fu-Yi & Wang, Ling, 2009. "Differential evolution algorithm-based parameter estimation for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2110-2118.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2110-2118
    DOI: 10.1016/j.chaos.2007.06.084
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    References listed on IDEAS

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    2. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Tang, Fang & Huang, De-Xian, 2006. "Directing orbits of chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 454-461.
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    Cited by:

    1. Tang, Yinggan & Guan, Xinping, 2009. "Parameter estimation of chaotic system with time-delay: A differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3132-3139.
    2. Li, Nianqiang & Pan, Wei & Yan, Lianshan & Luo, Bin & Xu, Mingfeng & Jiang, Ning & Tang, Yilong, 2011. "On joint identification of the feedback parameters for hyperchaotic systems: An optimization-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 198-207.
    3. Ma, Liang & Chen, Bin & Wang, Xiaodong & Zhu, Zhengqiu & Wang, Rongxiao & Qiu, Xiaogang, 2019. "The analysis on the desired speed in social force model using a data driven approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 894-911.
    4. Jafari, Sajad & Ahmadi, Atefeh & Panahi, Shirin & Rajagopal, Karthikeyan, 2018. "Extreme multi-stability: When imperfection changes quality," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 182-186.
    5. Ahmadi, Mohamadreza & Mojallali, Hamed, 2012. "Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1108-1120.
    6. Banerjee, Amit & Abu-Mahfouz, Issam, 2014. "A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 65-83.
    7. Coelho, Leandro dos Santos & Sauer, João Guilherme & Rudek, Marcelo, 2009. "Differential evolution optimization combined with chaotic sequences for image contrast enhancement," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 522-529.
    8. Strebel, Oliver, 2013. "A preprocessing method for parameter estimation in ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 93-104.
    9. Kaushal Kumar, 2023. "Data-driven modeling and parameter estimation of nonlinear systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(7), pages 1-13, July.
    10. Torres, Lizeth & Besançon, Gildas & Georges, Didier & Verde, Cristina, 2012. "Exponential nonlinear observer for parametric identification and synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 836-846.

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