Solutions to the Van der Pol Equation: a Model of Aortic Blood Flow

Atlas, Glen; Desiderio, Michael

doi:10.1109/nebc.2006.1629793

Cited by 3 publications

(2 citation statements)

References 5 publications

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“…4). An average increase in VTI with MUD was 3.29 cm using the formulae SV = πr 2 × VTI, with a normal aortic radius in the adult female being 1.16 cm, [13] and this translated to an average increase of 13.9 mL in SV. Therefore, CO increased by 1 112 mL/min (1.1 L/min) at an average HR of 80 for the study population (CO = SV × HR).…”

Section: Discussionmentioning

confidence: 97%

Impact of manual uterine displacement and left lateral tilt on echocardiographical velocity time intergral (stroke volume) in advanced pregnancy

et al. 2020

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Section: Discussionmentioning

confidence: 97%

Impact of manual uterine displacement and left lateral tilt on echocardiographical velocity time intergral (stroke volume) in advanced pregnancy

et al. 2020

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“…Liénard System can be and has been applied in various fields such as chemical reactions, radio and vacuum tube technology, electronic oscillators, lasers, predator-prey systems, growth of a single species, aortic blood flow, vibration analysis, etc. [6][7][8][9]. When the Van der Pol Oscillator or the Liénard Oscillator emerged, the semiconductor circuit elements were not yet available, but, today, a Liénard Oscillator can be implemented by using different types of semiconductor circuit elements such as the ones given in [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of schottky diode bridge and JFET based liénard oscillator circuit

ÇAKIR

2024

Sigma J Eng Nat Sci - Sigma Müh Fen Bil Derg

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Liénard Oscillator circuit has numerous variations. Nowadays, due to the developments of semiconductor technology, such an oscillator can be made using various semiconductor circuit elements. In this study, it has been shown that a Liénard Oscillator can also be made using a Schottky diode bridge and a JFET based nonlinear resistor. First, the new Liénard Oscillator topology is given, then, the dynamic model of the circuit is derived, and the simulations of the circuit are made. The currents, voltages and limit cycle of the Liénard Oscillator circuit are obtained with simulations using LTspice circuit analysis program. The simulations have confirmed that the circuit operates as a Liénard Oscillator.

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Van der Pol equation with sine nonlinearity: dynamical behavior and real time control to a target trajectory

Fonkou¹,

Louodop²,

Talla³

et al. 2021

Phys. Scr.

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In this work, the dynamical behavior and real time control of a target trajectory of a modified Van der Pol model so the potential is proportional to the term ( ) x sin n is proposed. A generalization in the case of small oscillations on the ( ) x sin n function is studied. Due to ( ) x sin n function, the system presents periodical regions of stability and unstability, a very rich dynamical behavior. Analytical investigations based on the harmonic balance method came out some specific values of the excitation frequency for which the model is subjected to a phenomenon of frequency entrainment. Also, under effect of the sine function power, chaos appears for even small value of the nonlinearity coefficient, in contrast to the classical Van der Pol oscillator. An investigation as an artificial pacemaker is done based on the real frequency of the natural pacemaker. We found that the modified Van der Pol model, like the classic Van der Pol model, can play the role of an artificial pacemaker with some approximations. Due to the complexity of the analogical sine function, an experimental study was made by real implementation of an Arduino Card based on the Runge-Kutta 4th order algorithm. The results obtained show a good correlation with the numerical results. RECEIVED

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Solutions to the Van der Pol Equation: a Model of Aortic Blood Flow

Cited by 3 publications

References 5 publications

Impact of manual uterine displacement and left lateral tilt on echocardiographical velocity time intergral (stroke volume) in advanced pregnancy

Impact of manual uterine displacement and left lateral tilt on echocardiographical velocity time intergral (stroke volume) in advanced pregnancy

Modeling and analysis of schottky diode bridge and JFET based liénard oscillator circuit

Van der Pol equation with sine nonlinearity: dynamical behavior and real time control to a target trajectory

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