GUDERMANNIAN NEURAL NETWORKS TO INVESTIGATE THE LIÉNARD DIFFERENTIAL MODEL

Bo Wang, Ye Wang, J. F. Gã“mez-Aguilar, Zulqurnain Sabir (), Muhammad Asif Zahoor Raja (), Hadi Jahanshahi (), Madini O. Alassafi () and Fawaz E. Alsaadi ()
Additional contact information
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. Gã“mez-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

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-17

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.

Keywords: Liénard Nonlinear System; Interior-Point Algorithm Technique; Numerical Performance; Genetic Algorithm; Artificial Neural Networks; Statistical Analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500505

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