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Parameter estimation for chaotic systems by particle swarm optimization

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  • He, Qie
  • Wang, Ling
  • Liu, Bo

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 multi-dimensional optimization problem. As a novel evolutionary computation technique, particle swarm optimization (PSO) 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 PSO for estimating parameters of chaotic systems. In this paper, a PSO approach is applied to estimate the parameters of Lorenz system. Numerical simulation and the comparisons demonstrate the effectiveness and robustness of PSO. Moreover, the effect of population size on the optimization performances is investigated as well.

Suggested Citation

  • He, Qie & Wang, Ling & Liu, Bo, 2007. "Parameter estimation for chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 654-661.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:654-661
    DOI: 10.1016/j.chaos.2006.03.079
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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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    1. He, Yao-Yao & Zhou, Jian-Zhong & Xiang, Xiu-Qiao & Chen, Heng & Qin, Hui, 2009. "Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3169-3176.
    2. 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.
    3. 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.
    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. Qasim M. Zainel & Saad M. Darwish & Murad B. Khorsheed, 2022. "Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations," Mathematics, MDPI, vol. 10(21), pages 1-21, November.
    6. Martín Alejandro Valencia-Ponce & Esteban Tlelo-Cuautle & Luis Gerardo de la Fraga, 2021. "Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    7. Berczyñski, Stefan & Kravtsov, Yury A. & Anosov, Oleg, 2009. "Chaotic dynamics reconstruction from noisy data: Phenomenon of predictability worsening for incomplete set of observables," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1459-1466.
    8. Alatas, Bilal & Akin, Erhan, 2009. "Chaotically encoded particle swarm optimization algorithm and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 939-950.
    9. Li, Chaoshun & Zhou, Jianzhong & Xiao, Jian & Xiao, Han, 2012. "Parameters identification of chaotic system by chaotic gravitational search algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 539-547.
    10. Xie, Bing & Ge, Fudong, 2023. "Parameters and order identification of fractional-order epidemiological systems by Lévy-PSO and its application for the spread of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. Tang, Yinggan & Cui, Mingyong & Li, Lixiang & Peng, Haipeng & Guan, Xinping, 2009. "Parameter identification of time-delay chaotic system using chaotic ant swarm," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2097-2102.
    12. Acharjee, P. & Mallick, S. & Thakur, S.S. & Ghoshal, S.P., 2011. "Detection of maximum loadability limits and weak buses using Chaotic PSO considering security constraints," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 600-612.
    13. Ning Ding & Hui Zhang & Tao Chen, 2017. "Simulation-based optimization of emergency evacuation strategy in ultra-high-rise buildings," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(3), pages 1167-1184, December.
    14. Shan, Bonan & Wang, Jiang & Deng, Bin & Zhang, Zhen & Wei, Xile, 2017. "Estimate the effective connectivity in multi-coupled neural mass model using particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 89-101.
    15. Tang, Yinggan & Guan, Xinping, 2009. "Parameter estimation for time-delay chaotic system by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1391-1398.
    16. 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.
    17. Strebel, Oliver, 2013. "A preprocessing method for parameter estimation in ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 93-104.

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