Designing Meyer wavelet neural networks for the three-species food chain model

Thanasak Mouktonglang; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Saira Bhatti; Thongchai Botmart; Wajaree Weera; Chantapish Zamart; Thanasak Mouktonglang; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Saira Bhatti; Thongchai Botmart; Wajaree Weera; Chantapish Zamart

doi:10.3934/math.2023003

AIMS Mathematics

2023, Volume 8, Issue 1: 61-75. doi: 10.3934/math.2023003

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Research article

Designing Meyer wavelet neural networks for the three-species food chain model

1.
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand
2.
Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai, 50200, Thailand
3.
Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE
4.
Department of Mathematics, Hazara University, Mansehra, Pakistan
5.
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, R.O.C
6.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad Pakistan
7.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 16 August 2022 Revised: 15 September 2022 Accepted: 22 September 2022 Published: 27 September 2022
MSC : 65K10, 92B20

The current research work is related to present the numerical solutions of three-species food chain model (TS-FCM) by exploiting the strength of Meyer wavelet neural networks (MWNNs) along with the global and local search competencies. The particle swarm optimization technique works as a global operator, while the sequential quadratic programming scheme is applied as a local operator for the TS-FCM. The nonlinear TS-FCM is dependent upon three categories, called consistent of prey populations, specialist predator and top predator. The optimization of an error-based fitness function is presented by using the hybrid computing efficiency of the global and local search schemes, which is designed through the differential form of the designed ordinary differential model and its initial conditions. The proposed results of the TS-FCM are calculated through the stochastic numerical techniques and further comparison is performed by the Adams method to check the exactness of the scheme. The absolute error in good ranges is performed, which shows the competency of the proposed solver. Moreover, different statistical procedures have also been used to check the reliability of the proposed stochastic procedure along with forty numbers of independent trials and 10 numbers of neurons.
- Meyer wavelet neural networks,
- food chain system,
- Adam scheme,
- sequential quadratic programming,
- statistical soundings,
- particle swarm optimization
Citation: Thanasak Mouktonglang, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Saira Bhatti, Thongchai Botmart, Wajaree Weera, Chantapish Zamart. Designing Meyer wavelet neural networks for the three-species food chain model[J]. AIMS Mathematics, 2023, 8(1): 61-75. doi: 10.3934/math.2023003

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Abstract

The current research work is related to present the numerical solutions of three-species food chain model (TS-FCM) by exploiting the strength of Meyer wavelet neural networks (MWNNs) along with the global and local search competencies. The particle swarm optimization technique works as a global operator, while the sequential quadratic programming scheme is applied as a local operator for the TS-FCM. The nonlinear TS-FCM is dependent upon three categories, called consistent of prey populations, specialist predator and top predator. The optimization of an error-based fitness function is presented by using the hybrid computing efficiency of the global and local search schemes, which is designed through the differential form of the designed ordinary differential model and its initial conditions. The proposed results of the TS-FCM are calculated through the stochastic numerical techniques and further comparison is performed by the Adams method to check the exactness of the scheme. The absolute error in good ranges is performed, which shows the competency of the proposed solver. Moreover, different statistical procedures have also been used to check the reliability of the proposed stochastic procedure along with forty numbers of independent trials and 10 numbers of neurons.

References

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