Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients

Fonkou, R. F.; Louodop, Patrick; Talla, Pierre Kisito; Woafo, P.

doi:10.1016/j.heliyon.2022.e10112

Cited by 5 publications

(5 citation statements)

References 47 publications

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“…FitzHugh and Nagumo also proposed an improvement on Van der Pol's model, seeking to provide a simpler and clearer description in qualitative terms [38]. Inspired by the work of Balthazar Van der Pol and Van der Mark in 1926 [39,40], there has also been a great deal of work on heart rate modeling, notably the work of Fonkou et al [41][42][43][44][45][46]. We might also mention the work of Moe et al [47].…”

Section: Introductionmentioning

confidence: 99%

On the heart rhythm analysis using a nonlinear dynamics perspective: analytical study and electronic simulation

Fonkou,

Kengne,

Wamba

et al. 2024

Phys. Scr.

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Biological systems are highly complex, so understanding them requires extensive analysis. Cardiac rhythms are one such analysis. These rhythms are linked to a complex dynamic system defined on the basis of the electrical activity of cardiac cells. This electrical activity is essential to human physiology, defining numerous behaviours that include normal or pathological rhythms, generally measured by the electrocardiogram (ECG). This article presents a mathematical model to describe the electrical activity of the heart, using a nonlinear dynamics perspective. The stability analysis of this model in its autonomous state, uni-directionally coupled, shows a very rich dynamical behaviour characterized by periodical regions of stability and unstability. The model studied makes it possible to construct synthetic ECGs. These ECGs demonstrate a variety of responses, including normal and pathological rhythms: ventricular flutter, ventricular fibrillation, ventricular tachycardia and ventricular extrasystole. A quantitative analysis of the model is also carried out using bifurcation diagrams and the corresponding maximum Lyapunov exponents. In addition, variations in sinus rhythm are described by a time-dependent frequency (a dynamic variable varying in a disordered manner or following a given law), representing transient disturbances. This type of situation can represent transitions between different pathological behaviours or between normal and pathological physiologies. In this respect, the perspective of nonlinear dynamics is used to describe cardiac rhythms, which makes it possible to represent normal or pathological behaviours. An electronic simulation performed with the OrCAD-Pspice software for a real implementation of the cardiac system is carried out. The results obtained are in agreement with those obtained numerically.

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Section: Introductionmentioning

confidence: 99%

On the heart rhythm analysis using a nonlinear dynamics perspective: analytical study and electronic simulation

Fonkou,

Kengne,

Wamba

et al. 2024

Phys. Scr.

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“…In order to study cardiac activity through its dynamics, researchers have modelled the conduction system of the heart as a network of self-oscillating elements modelled by nonlinear oscillators [ 34 ]; Aino-Maija [ [35] , [36] , [37] , [38] , [39] ]. The first oscillator modelling cardiac activity being the Van der Pol oscillator [ 23 , 40 ], in order to reduce the high order of the equations the modelling of the heart has been done by a large number of oscillators [ 41 , 42 ]. They propose a more appropriate description of the natural pacemaker and are reduced versions of the Van der Pol oscillator, including the Hodgkin-Huxley model [ 43 ], the FitzHugh and Nagumo model [ 44 ], the Grudzinsky-Zebrowsky model [ 45 ].…”

Section: Introductionmentioning

confidence: 99%

“…Fonkou et al study in Ref. [ 41 ] the dynamic behavior of the heart by nonlinear analyses only on the sinus node. In the same logic, Kuate and Fotsin [ 54 ] analyse the rhythm by an experimental study based on electronic components.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior analysis of the heart system by the bifurcation structures

Fonkou

Kengne

Kamgang

et al. 2023

Heliyon

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“…It is the starting point for the modelling of several other models of non-linear oscillators [34][35][36][37][38][39][40]. It has also been used to model artificial pacemakers [41,42], in neurophysiology [43], in seismology [44], in communication [45], and so on. Under the action of an external stimulus, the Van der Pol oscillator has a very rich dynamic drive [46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

et al. 2023

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The present work studies the dynamical behavior of the Van der Pol oscillator with sine nonlinearity oscillator subjected to the effects of non-sinusoidal excitations through the analysis of bifurcation structures. In this work, a modification of the classical Van der Pol oscillator is carried out by replacing the linear term x with the nonlinear term sinn (x) . The idea is to see the impact of the strength of this function on the appearance of chaotic dynamics for small and large values of the nonlinear dissipation term  . For this purpose, studies by numerical simulation and by analogue simulation are proposed. First, using nonlinear analysis tools, a similarity on the bifurcation sequences is observed despite a difference in the ranks of obtaining the particular behaviours and the bifurcation points. This study is confirmed by their respective maximum Lyapunov exponents. In a second step, a real implementation using microcontroller technology, which is motivated by the use of an artificial pacemaker, is carried out. For a more practical case, the excitation signal is generated by another microcontroller. The study shows a similarity with the results obtained numerically. Thirdly, in order to show that the model can be derived from mathematical modelling, an electronic simulation using OrCAD-Pspice software is also proposed. The results obtained are in qualitative agreement

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Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients

Cited by 5 publications

References 47 publications

On the heart rhythm analysis using a nonlinear dynamics perspective: analytical study and electronic simulation

On the heart rhythm analysis using a nonlinear dynamics perspective: analytical study and electronic simulation

Dynamical behavior analysis of the heart system by the bifurcation structures

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

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