Open Access

ARTICLE

A Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-III

Naret Ruttanaprommarin¹, Zulqurnain Sabir^2,3, Rafaél Artidoro Sandoval Núñez⁴, Emad Az-Zo’bi⁵, Wajaree Weera⁶, Thongchai Botmart^6,*, Chantapish Zamart⁶

1 Department of Science and Mathematics, Faculty of Industry and Technology, Rajamangala University of Technology Isan Sakonnakhon Campus, Sakonnakhon, 47160, Thailand
2 Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
3 Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE
4 Universidad Nacional Autónoma de Chota, Cajamarca, Perú
5 Department of Mathematics and Statistics, Mutah University, Mutah-Al Karak-Jordan
6 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

* Corresponding Author: Thongchai Botmart. Email:

Computers, Materials & Continua 2023, 74(3), 5915-5930. https://doi.org/10.32604/cmc.2023.034362

Received 14 July 2022; Accepted 14 October 2022; Issue published 28 December 2022

Abstract

The current research aims to implement the numerical results for the Holling third kind of functional response delay differential model utilizing a stochastic framework based on Levenberg-Marquardt backpropagation neural networks (LVMBPNNs). The nonlinear model depends upon three dynamics, prey, predator, and the impact of the recent past. Three different cases based on the delay differential system with the Holling 3^rd type of the functional response have been used to solve through the proposed LVMBPNNs solver. The statistic computing framework is provided by selecting 12%, 11%, and 77% for training, testing, and verification. Thirteen numbers of neurons have been used based on the input, hidden, and output layers structure for solving the delay differential model with the Holling 3^rd type of functional response. The correctness of the proposed stochastic scheme is observed by using the comparison performances of the proposed and reference data-based Adam numerical results. The authentication and precision of the proposed solver are approved by analyzing the state transitions, regression performances, correlation actions, mean square error, and error histograms.

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Keywords

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