Heuristic computing with active set method for the nonlinear Rabinovich-Fabrikant model

Zulqurnain Sabir; Dumitru Baleanu; Sharifah E Alhazmi; Salem Ben Said

doi:10.1016/j.heliyon.2023.e22030

Heuristic computing with active set method for the nonlinear Rabinovich-Fabrikant model

Heliyon. 2023 Nov 7;9(11):e22030. doi: 10.1016/j.heliyon.2023.e22030. eCollection 2023 Nov.

Authors

Zulqurnain Sabir^{1

2}, Dumitru Baleanu^{3

4

5

6}, Sharifah E Alhazmi⁷, Salem Ben Said⁸

Affiliations

¹ Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.
² Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
³ Department of Mathematics, Cankaya University, Ankara, Turkey.
⁴ Institute of Space Sciences, Magurele, Romania.
⁵ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
⁶ Near East University, Mathematics research center, Nicosia, 99138, North Cyprus, Mersin 10 Turkey.
⁷ Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca, USA.
⁸ Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, United Arab Emirates.

Abstract

The current study shows a reliable stochastic computing heuristic approach for solving the nonlinear Rabinovich-Fabrikant model. This nonlinear model contains three ordinary differential equations. The process of stochastic computing artificial neural networks (ANNs) has been applied along with the competences of global heuristic genetic algorithm (GA) and local search active set (AS) methodologies, i.e., ANNs-GAAS. The construction of merit function is performed through the differential Rabinovich-Fabrikant model. The results obtained through this scheme are simple, reliable, and accurate, which have been calculated to optimize the merit function by using the GAAS method. The comparison of the obtained results through this scheme and the conventional reference solutions strengthens the correctness of the proposed method. Ten numbers of neurons along with the log-sigmoid transfer function in the neural network structure have been used to solve the model. The values of the absolute error are performed around 10^-07 and 10^-08 for each class of the Rabinovich-Fabrikant model. Moreover, the reliability of the ANNs-GAAS approach is observed by using different statistical approaches for solving the Rabinovich-Fabrikant model.

Keywords: Active set method; Artificial neural networks; Genetic algorithm; Numerical solutions; Rabinovich-Fabrikant.