Generalized Bonhoeffer-van der Pol oscillator for modelling cardiac pulse: Preliminary results

Peluffo-Ordóñez, Diego H.; Rodriguez-Sotelo, J. L.; Revelo-Fuelagán, Edgardo Javier; Ospina-Aguirre, Carolina; Olivard-Tost, G.

doi:10.1109/ccac.2015.7345211

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…This is for example the case of the van der Pol (VdP) system which was, first, introduced in order to describe triode oscillations in electrical circuits [1], and which was also later used in both the physical and biological sciences [2,3]. Similarly, the Bonhoeffer-van der Pol (BVdP) system was also designed to describe a class of excitable oscillatory systems including the Hodghin-Huxley model of the squid giant axon and have successfully used to reproduce the physiological states of nerve fiber namely, the resting state, active, refractory, enhanced and depressed states [3], and can be also adapted to describe action potential and normal cardiac pulse [4], to just name this few cases. Many other oscillators have been also introduced in the literature where the most popular are the basic Colpitts oscillator which is the combination of a transistor amplifier and LC circuits used to feedback the output signal [5,6], and the Chua oscillator [7,8].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…Nonlinear vibrations occur in countless areas, like vehicle dynamics [5], transportation [6], machine tools [7] or electrical devices [8]. With simple nonlinear oscillators, like the Van der Pol oscillators complex systems and phenomena [9]- [13] have already been modeled. In this paper nonlinear oscillators are examined with numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Numerical examination of nonlinear oscillators

Hajdú

2018

Pollack Periodica

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The numerical examination of nonlinear oscillators is presented in this paper. First some methods of nonlinear system modeling are described then the numerical creation of phaseplane, bifurcation diagrams and Poincaré sections are expounded in detail. The next part of the paper is the numerical examination of nonlinear oscillators, like the Duffing-Holmes oscillator and a mechatronic semi-active suspension system. The paper concludes with further development tasks.

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“…It has also found its ways to marine applications such as ship propeller blade number recognition as shown by Wang et al in [8]. Van der Pol oscillator has had less application examples than the Duffing oscillator nevertheless it still found its way into numerous domains such as in the medical field where was used in the modelling of the cardiac pulse as shown in [9]. Another example is the use of the Van der Pol oscillator in the modeling of the dust density wave fields as shown in [10].…”

Section: Related Workmentioning

confidence: 99%

Nonlinear Control of Chaotic Forced Duffing and Van der Pol Oscillators

Alghassab¹,

Mahmoud²,

Zohdy³

2017

IJMNTA

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This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator is added to both models to expand on the chaotic behavior of the oscillators. In order to control the system without comprising linearization, Lyapunov non-linear control was used. A control Lyapunov function was tailored to the system. This led to improved maneuverability of the controller and the performance of the overall system. The controller was found to be highly efficient in system tracking and had swift response time. Simulations were performed on both the uncontrolled and controlled cases. Both simulation results ultimately confirmed the effectiveness of the proposed controller.

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Generalized Bonhoeffer-van der Pol oscillator for modelling cardiac pulse: Preliminary results

Cited by 4 publications

References 13 publications

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

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

Numerical examination of nonlinear oscillators

Nonlinear Control of Chaotic Forced Duffing and Van der Pol Oscillators

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