An analysis of heart rhythm dynamics using a three-coupled oscillator model

Gois, Sandra R.F.S.M.; Savi, Marcelo A.

doi:10.1016/j.chaos.2008.09.040

Cited by 117 publications

(81 citation statements)

References 24 publications

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“…In addition, external stimulation is entered into the system, considering periodic stimulus sentence to each oscillator. This developed model can be shown by a system of differential equations as shown below, in which a Vander pol equation has been considered to model oscillator and another one to model the oscillator and the third one to model oscillator [7]:…”

Section: Three-oscillator Modelling Of the Heart Without Time Delaymentioning

confidence: 99%

“…Since even small delays may change the dynamics of the system, including of time delay in differential equations can cause drastic changes and chaos in a system that has regular behavior [7,13]. Thus, system (1) is changed as below in which represents time delay and = ( − ): By substitution, we will have Now, by applying the appropriate controller on it which is as follows [14]:…”

Section: Three-oscillator Modelling Of the Heart With Time Delaymentioning

confidence: 99%

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A New Three-Oscillator Model for the Heart System in the Case of Time Delay and Designing Appropriate Controller for Its Synchronization

Nazari

Heydari

Tavakoli

et al. 2014

ISRN Applied Mathematics

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If the and oscillators are not synchronized, it may arise some kinds of blocking arrhythmias in the system of heart. In this paper, in order to examine the heart system more precisely, we apply the three-oscillator model of the heart system, and to prevent arrhythmias, perform the following steps. Firstly, we add a voltage with rang 1 and frequency to node. Then, we use delay time factor in oscillators and finally the appropriate control is designed. In this paper, we have explained how simulating and curing these arrhythmias are possible by designing a three-oscillator system for heart in the state of delay and without delay and by applying an appropriate control. In the end, we present the simulation results.

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Section: Three-oscillator Modelling Of the Heart Without Time Delaymentioning

confidence: 99%

Section: Three-oscillator Modelling Of the Heart With Time Delaymentioning

confidence: 99%

A New Three-Oscillator Model for the Heart System in the Case of Time Delay and Designing Appropriate Controller for Its Synchronization

Nazari

Heydari

Tavakoli

et al. 2014

ISRN Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…It is arguable that the presence of P-wave in Figure 6 is very small. In a recent study [2], a three coupled oscillator based model successfully reproduced both the P and T waves, under healthy condition only, but its generalization for wide variety of pathological ECG is not known till date and needs further exploration.…”

Section:  mentioning

confidence: 99%

“…The fundamental principle behind generation of any complex biological waveform is governed by few set of nonlinear differential equations. Several dynamical system theoretic approaches have been proposed to mathematically model ECG waveform and the action potentials, generated in different nodes of human heart [2]. Various arguments are reported in the literature, for example by Babloyantz and Destexhe [3], about the fact whether the heart perfectly behaves like a periodic oscillator or not.…”

Section: Introductionmentioning

confidence: 99%

Fractional dynamical model for the generation of ECG like signals from filtered coupled Van-der Pol oscillators

Das

Maharatna

2013

Computer Methods and Programs in Biomedicine

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In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators, which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ECG like signal.

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“…In this paper, we consider the synchronization of coupled nonlinear oscillators in networked systems, which finds its motivation in the study of a wide range of applications spanning from large scale systems in nature (e.g. brain dynamics [7], [15], cardiac pacemakers [8]) to human-related artificial networks (e.g. collective swarm motion [13], smart grids [6]).…”

Section: Introductionmentioning

confidence: 99%

On the synchronization of spatially coupled oscillators

Cenedese

Favaretto

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-Over the past decade, considerable attention has been devoted to the problem of emergence of synchronization patterns in a network of coupled oscillators, which can be observed in a variety of disciplines, from the biological to the engineering fields. In this context, the Kuramoto model is a classical model for describing synchronization phenomena that arise in large-scale systems that exploit local information and interactions. In this work, an extension of such a model is presented, that considers the spatial distances among the oscillator nodes. In detail, coupling strength and spatial conditions are derived, needed to reach phase cohesiveness and frequency synchronization, both in the scenario when a single population of agents is present and when two different populations interact. These theoretical findings are confirmed by extensive numerical Monte Carlo simulations and statistical analysis.

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An analysis of heart rhythm dynamics using a three-coupled oscillator model

Cited by 117 publications

References 24 publications

A New Three-Oscillator Model for the Heart System in the Case of Time Delay and Designing Appropriate Controller for Its Synchronization

A New Three-Oscillator Model for the Heart System in the Case of Time Delay and Designing Appropriate Controller for Its Synchronization

Fractional dynamical model for the generation of ECG like signals from filtered coupled Van-der Pol oscillators

On the synchronization of spatially coupled oscillators

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