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Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model

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Abstract

In this work, an intelligent computing algorithm is developed for finding the approximate solution of heart model based on nonlinear Van der Pol (VdP)-type second-order ordinary differential equations (ODEs) using feed-forward artificial neural networks (FF-ANNs) optimized with genetic algorithms (GAs) hybrid through interior-point algorithm (IPA). The mathematical modeling of the system is constructed using FF-ANN models by defining an unsupervised error and unknown weights; the networks are tuned globally with GAs, and local refinement of the results is made with IPA. Design scheme is applied to study the VdP heart dynamics model by varying the pulse shape modification factor, damping coefficients and external forcing factor while keeping the fixed value of the ventricular contraction period. The results of the proposed algorithm are compared with reference numerical solutions of Adams method to establish its correctness. Multiple independent runs are performed for the scheme, and results of statistical analyses in terms of mean absolute deviation, root-mean-square error and Nash–Sutcliffe efficiency illustrate its applicability, effectiveness and reliability.

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Acknowledgement

The authors would like to express their appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. COS/IRG-09/15.

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Authors and Affiliations

  1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan

    Muhammad Asif Zahoor Raja & Fiaz Hussain Shah

  2. Department of Mathematical Sciences, UAEU, P O Box 15551, Al-Ain, United Arab Emirates

    Muhammad Ibrahim Syam

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  1. Muhammad Asif Zahoor Raja
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  2. Fiaz Hussain Shah
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  3. Muhammad Ibrahim Syam
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Correspondence to Muhammad Asif Zahoor Raja.

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Raja, M.A.Z., Shah, F.H. & Syam, M.I. Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model. Neural Comput & Applic 30, 3651–3675 (2018). https://doi.org/10.1007/s00521-017-2949-0

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