Cardiac Pulse Modeling Using a Modified van der Pol Oscillator and Genetic Algorithms

Lopez-Chamorro, Fabián M.; Arciniegas-Mejia, Andrés F.; Imbajoa-Ruiz, David Esteban; Rosero-Montalvo, Paúl D.; García, Pedro J.; Castro-Ospina, Andrés Eduardo; Acosta, Antonio; Peluffo-Ordóñez, Diego H.

doi:10.1007/978-3-319-78723-7_8

Cited by 2 publications

(3 citation statements)

References 15 publications

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“…A classical representation of the Van der Pol oscillator is in oscillator triode circuits [21]. This equation is also used to describe the Cardiac Pulse Modeling [22]. Another well-known nonlinear equation is Mathieu's equation.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Oscillators

Hou

Qie

et al. 2021

FU Mech Eng

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Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations describing the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute more precisely their nonlinear frequencies. The nonlinear vibration process of a conservative oscillator always follows the law of energy conservation. A variational formulation is constructed and its Hamiltonian invariant is obtained. This paper suggests a Hamiltonian-based formulation to quickly determine the frequency property of the nonlinear oscillator. An example is given to explicate the solution process.

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Section: Introductionmentioning

confidence: 99%

Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Oscillators

Hou

Qie

et al. 2021

FU Mech Eng

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show abstract

“…In fact by setting a < 0, b > 0, e > 0 and d = − f = 1, equation (4) reduces to the model with four parameters describing the nonlinear dissipative dynamics of a chemical reaction in which coefficients a, b and c are related respectively to the characteristic evolution time of feedback, the second constraint on which feedback values depend and to the first constraint parameter [31]. Similarly, by making use of the appropriate change of variables namely x = X − x e and y = Y − y e where x e and y e are the equilibrium point of the system (4), one recovers the modified VdP equation introduced by Grudziński and Żebrowski [30] and Lopez-Chamorro et al [33] modelling the cardiac pulses and pacemaker. The coefficients of this equation have been obtained by means of the optimization procedure which were consisted to align the system response after the optimization process to the waveform normal heartbeat represented by the preprocessed ECG signal for different heartbeat samples [33].…”

Section: Model Description and State Equationsmentioning

confidence: 91%

“…Similarly, by making use of the appropriate change of variables namely x = X − x e and y = Y − y e where x e and y e are the equilibrium point of the system (4), one recovers the modified VdP equation introduced by Grudziński and Żebrowski [30] and Lopez-Chamorro et al [33] modelling the cardiac pulses and pacemaker. The coefficients of this equation have been obtained by means of the optimization procedure which were consisted to align the system response after the optimization process to the waveform normal heartbeat represented by the preprocessed ECG signal for different heartbeat samples [33].…”

Section: Model Description and State Equationsmentioning

confidence: 99%

Control of self-sustained oscillatory behavior in the dynamics of generalized Bonhoeffer-van der Pol system: Effect of asymmetric parameter

Sonna¹,

Yémélé²

2021

Phys. Scr.

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A generalized form of the autonomous Bonhoeffer-van der Pol (BVdP) system described by a second-order dynamical system with six independent parameters consistent with its optimal mathematical modeling, instead of three usually used, is investigated. Through its equivalent form, the generalized asymmetric van der Pol-Duffing (GAVdPD) system and the steady states of this system are derived. The analysis show that the system may exhibit one or three steady states when it is driven by an external constant impulse taken as a main control parameter. Domain ranges in which the system can function as well as monostable system as a bistable system are derived. In addition, by means of the theory of Hopf Bifurcation, it appears that there are large possibilities for the system to work as self-sustained oscillator, forced oscillator or other possibilities for which the system does not operate, indicating the richness of this generalized form of the BVdP system. Limit cycle solutions are derived at the neighboring of the Andronov-Hopf Bifurcation points even for large values of the asymmetric parameter. All these results are checked through numerical simulations. Applying these analytical investigations to the electronic circuit executing the dynamics of the basic BVdP system, two distinct working regimes are highlighted, depending on the magnitude of the capacitance with respect to a threshold value function of the characteristic parameters both of the self and of the nonlinear resistance. Through PSPICE simulations the accuracy of these analytical and numerical investigations have been confirmed.

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Cardiac Pulse Modeling Using a Modified van der Pol Oscillator and Genetic Algorithms

Cited by 2 publications

References 15 publications

Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Oscillators

Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Oscillators

Control of self-sustained oscillatory behavior in the dynamics of generalized Bonhoeffer-van der Pol system: Effect of asymmetric parameter

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