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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Semi-analytical Nonlinear Firing Dynamics of a Heartbeating Model

Journal of Applied Nonlinear Dynamics 14(1) (2025) 233--246 | DOI:10.5890/JAND.2025.03.015

Xinya Wang, Yeyin Xu, Ying Wu

School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an, 710049, PR China

State Key laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an,

710049, PR China

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Abstract

Nonlinear heartbeating dynamics have become a hot issue nowadays. More and more attention has been drawn on the nonlinearity of the heartbeating models. Previous studies adopted numerical integration method and cared more about the single solutions or time-series results. Based on a discrete mapping method, this study deals with the semi-analytical solutions and stability of a heartbeating model consisted of coupled van der Pol oscillators. The heartbeating model is discretized to form implicit mappings by a midpoint scheme. Nonlinear firing characteristics varying with the excitation frequency, such as stability and bifurcation, are predicted by eigenvalue analysis. Stable and unstable heartbeating waveforms are illustrated through bifurcation and phase diagram to provide dynamic information for situation where arrhythmia may occur. Global and independent firing waveforms are discovered and distinguished in the study. Independent period-2 and 3 firing waveforms are solitary and limited by saddle node bifurcations. The results, especially the period-doubling bifurcations and the unstable action potential waveforms obtained based on the discrete mapping method, can be referred in clinical treatment.

Acknowledgments

This work is supported by the National Nature Science Foundation of China (Grant No. 12102319).

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