Dynamical behavior analysis of the heart system by the bifurcation structures

Fonkou, R. F.; Kengne, Romanic; Kamgang, Herton Carel Fotsing; Talla, Pierre Kisito

doi:10.1016/j.heliyon.2023.e12887

Cited by 4 publications

(8 citation statements)

References 67 publications

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“…Periodic windows are found inbetween the region. Therefore, an antimonotonicity phenomenon is displayed VCSELCM [25][26][27][28][29][30]. The dynamical behaviors spotted in figures 2(a1) and (a2) are endorsed by the LLE of figure 2(b).…”

Section: Analytical and Numerical Analysis Of Vcseslcmmentioning

confidence: 84%

“…To prove the practical feasibility and validate the dynamical behavior found in the previous subsection, a microcontroller implementation of VCSELCM whose description is given by system (1) is designed and tested in this subsection. The microcontroller implementation of some dynamical systems can be found in [30][31][32][33]. The experimentation platform of figure 6 consists of an Arduino Mega 2560 board building up the system, a two R/ 2R resistors system operating as DACs and an Arduino Uno board coupled to a computer for signal acquisition and display.…”

Section: Microcontroller Validation Of Vcselcmmentioning

confidence: 99%

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Pseudo random number generator based on vertical-cavity surface-emitting lasers under current modulation embedded in microcontroller

Sundarambal¹,

Kuate

Abba

et al. 2023

Phys. Scr.

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This paper explores the dynamics, microcontroller validation of a vertical-cavity surface-emitting laser (VCSEL) under current modulation (CM) and employs it to model a process of pseudo-random number generator (PRNG). Solitary VCSEL has three equilibrium points whose stabilities depend on the direct current density. VCSEL under CM (VCSELCM) experiences antimonotonicity, chaotic bubble attractor as well as chaotic attractor. A microcontroller implementation of VCSELCM is used to establish the dynamical behaviors spotted in VCSELCM during the numerical simulations. Lastly, the chaotic characteristics depicted by the VCSELCM are used to design a process of PRNG. The generated random bits are validated successfully by a standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22).

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Section: Analytical and Numerical Analysis Of Vcseslcmmentioning

confidence: 84%

Section: Microcontroller Validation Of Vcselcmmentioning

confidence: 99%

Pseudo random number generator based on vertical-cavity surface-emitting lasers under current modulation embedded in microcontroller

Sundarambal¹,

Kuate

Abba

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

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“…T is the delay and ( )  x t the derivative of ( ) x t . By introducing relation (8) into system (7), we obtain the system (9). Using Cardran's method [56], system (9) is solved.…”

Section: Fixed Points Analysismentioning

confidence: 99%

“…Physiologically, normal compliance of the heart depends on the regularity of the system. References [9][10][11][12][13] have shown that the construction of synthetic ECGs can reveal a variety of responses, including normal and pathological rhythms. In a similar vein, Norbert Wiener and Arturo Rosenblueth, in their work on the mathematical formulation of the problem of impulse conduction in a network of connected excitable elements, notably in cardiac muscle, demonstrated the importance of the spatial role of depolarization waves on cardiac tissue, beyond just the SA and AV nodes, and the His bundles and Purkinje fibers [14].…”

Section: Introductionmentioning

confidence: 99%

“…Using nonlinearities and randomness, Cheffer and Savi also propose a nonlinear dynamics perspective for analyzing heart rate [51]. References [9,39] also show that heart rate analysis can be performed numerically using non-linear analysis tools, using bifurcation curves associated with their respective maximum Lyapunov exponents. These studies provide a better analysis of the choice of parameters.…”

Section: Introductionmentioning

confidence: 99%

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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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Modeling of self-oscillating flexible circuits based on liquid crystal elastomers

Liu,

Shi,

Song

et al. 2024

International Journal of Mechanical Sciences

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Dynamical behavior analysis of the heart system by the bifurcation structures

Cited by 4 publications

References 67 publications

Pseudo random number generator based on vertical-cavity surface-emitting lasers under current modulation embedded in microcontroller

Pseudo random number generator based on vertical-cavity surface-emitting lasers under current modulation embedded in microcontroller

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

Modeling of self-oscillating flexible circuits based on liquid crystal elastomers

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