Supervised neural learning for the predator-prey delay differential system of Holling form-III

Naret Ruttanaprommarin; Zulqurnain Sabir; Salem Ben Said; Muhammad Asif Zahoor Raja; Saira Bhatti; Wajaree Weera; Thongchai Botmart; Naret Ruttanaprommarin; Zulqurnain Sabir; Salem Ben Said; Muhammad Asif Zahoor Raja; Saira Bhatti; Wajaree Weera; Thongchai Botmart

doi:10.3934/math.20221101

AIMS Mathematics

2022, Volume 7, Issue 11: 20126-20142. doi: 10.3934/math.20221101

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Research article

Supervised neural learning for the predator-prey delay differential system of Holling form-III

1.
Department of Science and Mathematics, Faculty of Industry and Technology, Rajamangala University of Technology Isan Sakonnakhon Campus, Sakonnakhon 47160, Thailand
2.
Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE
3.
Department of Mathematics, Hazara University, Mansehra, Pakistan
4.
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan
5.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad Pakistan
6.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 05 July 2022 Revised: 22 August 2022 Accepted: 30 August 2022 Published: 13 September 2022
MSC : 92B20, 34A34

The purpose of this work is to present the stochastic computing study based on the artificial neural networks (ANNs) along with the scaled conjugate gradient (SCG), ANNs-SCG for solving the predator-prey delay differential system of Holling form-III. The mathematical form of the predator-prey delay differential system of Holling form-III is categorized into prey class, predator category and the recent past effects. Three variations of the predator-prey delay differential system of Holling form-III have been numerical stimulated by using the stochastic ANNs-SCG procedure. The selection of the data to solve the predator-prey delay differential system of Holling form-III is provided as 13%, 12% and 75% for testing, training, and substantiation together with 15 neurons. The correctness and exactness of the stochastic ANNs-SCG method is provided by using the comparison of the obtained and data-based reference solutions. The constancy, authentication, soundness, competence, and precision of the stochastic ANNs-SCG technique is performed through the analysis of the correlation measures, state transitions (STs), regression analysis, correlation, error histograms (EHs) and MSE.
- time delay,
- Holling form-III,
- mathematical system,
- artificial neural networks,
- scaled conjugate gradient
Citation: Naret Ruttanaprommarin, Zulqurnain Sabir, Salem Ben Said, Muhammad Asif Zahoor Raja, Saira Bhatti, Wajaree Weera, Thongchai Botmart. Supervised neural learning for the predator-prey delay differential system of Holling form-III[J]. AIMS Mathematics, 2022, 7(11): 20126-20142. doi: 10.3934/math.20221101

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Abstract

The purpose of this work is to present the stochastic computing study based on the artificial neural networks (ANNs) along with the scaled conjugate gradient (SCG), ANNs-SCG for solving the predator-prey delay differential system of Holling form-III. The mathematical form of the predator-prey delay differential system of Holling form-III is categorized into prey class, predator category and the recent past effects. Three variations of the predator-prey delay differential system of Holling form-III have been numerical stimulated by using the stochastic ANNs-SCG procedure. The selection of the data to solve the predator-prey delay differential system of Holling form-III is provided as 13%, 12% and 75% for testing, training, and substantiation together with 15 neurons. The correctness and exactness of the stochastic ANNs-SCG method is provided by using the comparison of the obtained and data-based reference solutions. The constancy, authentication, soundness, competence, and precision of the stochastic ANNs-SCG technique is performed through the analysis of the correlation measures, state transitions (STs), regression analysis, correlation, error histograms (EHs) and MSE.

References

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