IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i5p3132-3139.html
   My bibliography  Save this article

Parameter estimation of chaotic system with time-delay: A differential evolution approach

Author

Listed:
  • Tang, Yinggan
  • Guan, Xinping

Abstract

It is an important issue to estimate parameters of chaotic system in nonlinear science. In this paper, parameter estimation problem of chaotic system with time-delay is considered. Parameters and time-delay are estimated together by treating time-delay as an additional parameter. The parameter estimation problem is converted to an multi-dimensional optimization problem. A differential evolution (DE) algorithm, which possess a powerful searching capability for finding the solutions for a given optimization problem, is applied to solve this optimization problem. Two illustrative examples are given to verify the effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3132-3139
    DOI: 10.1016/j.chaos.2009.04.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909003981
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.04.045?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Rakshit, Biswambhar & Chowdhury, A. Roy & Saha, Papri, 2007. "Parameter estimation of a delay dynamical system using synchronization in presence of noise," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1278-1284.
    4. 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.
    5. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong, 2005. "A unified approach for impulsive lag synchronization of chaotic systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1177-1184.
    6. Shen, Liqun & Wang, Mao, 2008. "Robust synchronization and parameter identification on a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 106-111.
    7. Li, Lixiang & Yang, Yixian & Peng, Haipeng & Wang, Xiangdong, 2006. "Parameters identification of chaotic systems via chaotic ant swarm," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1204-1211.
    8. Ge, Z.-M. & Cheng, J.-W., 2005. "Chaos synchronization and parameter identification of three time scales brushless DC motor system," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 597-616.
    9. Lu, Jianquan & Cao, Jinde, 2007. "Synchronization-based approach for parameters identification in delayed chaotic neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 672-682.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Tarai (Poria), Anindita & Poria, Swarup & Chatterjee, Prasanta, 2009. "Synchronization of bidirectionally coupled chaotic Chen’s system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 190-197.
    9. 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.
    10. Strebel, Oliver, 2013. "A preprocessing method for parameter estimation in ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 93-104.
    11. 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.
    12. Márquez-Martínez, L.A. & Cuesta-García, J.R. & Pena Ramirez, J., 2022. "Boosting synchronization in chaotic systems: Combining past and present interactions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    13. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.
    14. 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.
    15. Li, Yuying & Wen, Qiaoyan & Li, Lixiang & Peng, Haipeng, 2009. "Hybrid chaotic ant swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 880-889.
    16. Lü, Ling & Wei, Qingtao & Jia, Hao & Tian, Shuo & Xu, Zhao & Zhao, Lina & Xu, Zhichao & Xu, Xianying, 2019. "Parameter identification and synchronization between uncertain delay networks based on the coupling technology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    17. Yassen, M.T., 2008. "Synchronization hyperchaos of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 465-475.
    18. Song, Xinlin & Wang, Chunni & Ma, Jun & Ren, Guodong, 2016. "Collapse of ordered spatial pattern in neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 95-112.
    19. 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.
    20. Hong, Wei-Chiang, 2010. "Application of chaotic ant swarm optimization in electric load forecasting," Energy Policy, Elsevier, vol. 38(10), pages 5830-5839, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3132-3139. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.