IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i03ns0218348x22500505.html
   My bibliography  Save this article

Gudermannian Neural Networks To Investigate The Liã‰Nard Differential Model

Author

Listed:
  • BO WANG

    (School of Electronic Information and Automation, Aba Teachers University, Wenchuan 623002, P. R. China†School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu 610054, P. R. China)

  • YE WANG

    (��Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P. R. China)

  • J. F. GÓMEZ-AGUILAR

    (�CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos, Mexico¶Consejo Académico, Universidad Virtual CNCI, Monterrey, México)

  • ZULQURNAIN SABIR

    (��Department of Mathematics and Statistics, Hazara University Mansehra, KKH Dhodiyal, Mansehra 21120, Khyber Pakhtunkhwa, Pakistan)

  • MUHAMMAD ASIF ZAHOOR RAJA

    (*Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, R. O. C.)

  • HADI JAHANSHAHI

    (��†Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 5V6, Canada)

  • MADINI O. ALASSAFI

    (��‡Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia)

  • FAWAZ E. ALSAADI

    (��‡Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia)

Abstract

The aim of this study is to present the numerical solutions of the Liénard nonlinear model by designing the structure of the computational Gudermannian neural networks (GNNs) along with the global/local search efficiencies of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e. GNNs–GAs–IPA. A merit function in terms of differential system and its boundary conditions is designed and optimization is performed by using the proposed computational procedures of GAs–IPA to solve the Liénard nonlinear differential system. Three different highly nonlinear examples based on the Liénard differential system have been tested to check the competence, exactness and proficiency of the proposed computational paradigm of GNNs–GAs–IPA. The statistical performances in terms of different operators have been provided to check the reliability, consistency and stability of the computational GNNs–GAs–IPA. The plots of the absolute error, performance measures, results comparison, convergence analysis based on different operators, histograms and boxplots are also illustrated. Moreover, statistical gauges using minimum, mean, maximum, semi-interquartile range, standard deviation and median are also provided to authenticate the optimal performance of the GNNs–GAs–IPA.

Suggested Citation

  • Bo Wang & Ye Wang & J. F. Gã“Mez-Aguilar & Zulqurnain Sabir & Muhammad Asif Zahoor Raja & Hadi Jahanshahi & Madini O. Alassafi & Fawaz E. Alsaadi, 2022. "Gudermannian Neural Networks To Investigate The Liã‰Nard Differential Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-17, May.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500505
    DOI: 10.1142/S0218348X22500505
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22500505
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22500505?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.

    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:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500505. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/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.