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Swarming Computational Approach for the Heartbeat Van Der Pol Nonlinear System

Muhammad Umar1, Fazli Amin1, Soheil Salahshour2, Thongchai Botmart3, Wajaree Weera3, Prem Junswang4,*, Zulqurnain Sabir1

1 Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2 Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
3 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
4 Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

* Corresponding Author: Prem Junswang. Email:

Computers, Materials & Continua 2022, 72(3), 6185-6202.


The present study is related to design a stochastic framework for the numerical treatment of the Van der Pol heartbeat model (VP-HBM) using the feedforward artificial neural networks (ANNs) under the optimization of particle swarm optimization (PSO) hybridized with the active-set algorithm (ASA), i.e., ANNs-PSO-ASA. The global search PSO scheme and local refinement of ASA are used as an optimization procedure in this study. An error-based merit function is defined using the differential VP-HBM form as well as the initial conditions. The optimization of the merit function is accomplished using the hybrid computing performances of PSO-ASA. The designed performance of ANNs-PSO-ASA is implemented for the numerical treatment of the VP-HBM dynamics by fluctuating the pulse shape adjustment terms, external forcing factor and damping coefficient with fixed ventricular contraction period. To perform the correctness of the present scheme, the obtained numerical results through the designed ANN-PSO-ASA will be compared with the Adams numerical method. The statistical investigations with larger dataset are provided using the “mean absolute deviation”, “Theil’s inequality coefficient” and “variance account for” operators to perform the applicability, reliability, and effectiveness of the designed ANNs-PSO-ASA scheme for solving the VP-HBM.


Cite This Article

M. Umar, F. Amin, S. Salahshour, T. Botmart, W. Weera et al., "Swarming computational approach for the heartbeat van der pol nonlinear system," Computers, Materials & Continua, vol. 72, no.3, pp. 6185–6202, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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