{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T14:10:43Z","timestamp":1783433443481,"version":"3.54.6"},"reference-count":43,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,6,15]]},"abstract":"<jats:p> The aim of this work is to investigate the nonlinear dynamics of a forced cardiac pacemaker model represented by a forced modified van der Pol oscillator by using the method of harmonic balance and the method of multiple time scales. The amplitudes of the forced harmonic, primary resonant state, super-harmonic and sub-harmonic resonant state oscillations are obtained and the effects of some system parameters on these amplitudes are investigated; hysteresis and jump phenomena are found. Three similar oscillators are then coupled together via time-delay coupling to model the heart rhythm and the effect of the coupling factor and time delay is also investigated. The overall model is then discretized using the fourth-order Runge\u2013Kutta algorithm. A corresponding very high-speed integrated circuit hardware description language code is then written, synthesised and implemented using the Vivado-2017.4 software for the Artix7-xc7a35tftg256-1 field programmable gate array chip. The chip statistics, time series electrocardiograms and phase portraits of the model are derived; a good correlation between theoretical results (obtained with MATLAB program and Vivado software) and practical results is observed. <\/jats:p>","DOI":"10.1142\/s0218127422501061","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T07:22:53Z","timestamp":1655191373000},"source":"Crossref","is-referenced-by-count":5,"title":["Multiple Time-Scales Dynamics of a Cardiac Pacemaker Model with Application to Heart Rhythm Modeling: Theoretical Study and FPGA Implementation"],"prefix":"10.1142","volume":"32","author":[{"given":"Guy Chance","family":"Gildas Kuate","sequence":"first","affiliation":[{"name":"Unit\u00e9 de Recherche de Mati\u00e8re Condens\u00e9e, d\u2019Electronique et de Traitement du Signal (UR-MACETS), Department of Physics, University of Dschang, P. O. Box 67, Dschang, Cameroon"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeanne Sandrine","family":"Mabekou Takam","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche de M\u00e9canique, et de Mod\u00e9lisation des Syst\u00e8mes Physiques (UR2MSP), Department of Physics, University of Dschang, P. O. Box 67, Dschang, Cameroon"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frank Xavier","family":"Ngagoum Tchamdjeu","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche de Mati\u00e8re Condens\u00e9e, d\u2019Electronique et de Traitement du Signal (UR-MACETS), Department of Physics, University of Dschang, P. O. 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