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Parameter identification of Chen and Lü systems: A differential evolution approach

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  • Chang, Wei-Der

Abstract

This paper presents a novel differential evolution (DE) algorithm to solve the identification problem for Chen and Lü systems. A collection of unknown system parameters of Chen and Lü systems is taken as a manipulated parameter vector, and will be optimally evolved to approximate the actual parameters by using the proposed DE algorithm. Basically, the DE algorithm comprises three main operators of mutation, crossover, and selection to achieve the evolution. In the meanwhile, a cost function defined for solving the identification problem of chaotic systems is also minimized. Two illustrative examples are given to show the validity of the proposed method.

Suggested Citation

  • Chang, Wei-Der, 2007. "Parameter identification of Chen and Lü systems: A differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1469-1476.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1469-1476
    DOI: 10.1016/j.chaos.2005.11.067
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    References listed on IDEAS

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    1. Yassen, M.T., 2005. "Adaptive synchronization of Rossler and Lü systems with fully uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1527-1536.
    2. Kim, Jae-Hun & Park, Chang-Woo & Kim, Euntai & Park, Mignon, 2005. "Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1353-1361.
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Coelho, Leandro dos Santos, 2009. "Reliability–redundancy optimization by means of a chaotic differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 594-602.

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