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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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    2. 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.
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    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.
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    13. 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.
    14. 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.
    15. 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.
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