Kaplan Oscillator Configuration by Means of Bifurcation Diagrams to Generate the P and T Waves, in Addition QRS Complex of the ECG

Abstract

In this article, we examine the oscillator system developed by Kaplan that generates electrocardiogram signals ECG. The system consists of two sets coupled in a ring. Each set has a Van der Pol oscillator, a differential delay equation and a low-pass half-wave filter. The ECG is composed of the P wave, the QRS complex and the T wave. The Kaplan oscillator generates only the QRS complex, this with two different amplitudes of the R-wave and non-uniform time spacing. The damping parameter of the Van der Pol oscillator, epsilon e and the filter’s T parameter were analysed, by means of bifurcation diagrams, in order to generate the other ECG oscillations. We created a new parameter, called gamma γ, which was included in the mathematical model. This reduces the amplitude of the Van der Pol oscillator signal derivative and consequently affects the filter performance and the differential delay equation. Our new configuration obtained through analysis generates the QRS complex with constant R-wave amplitude and also constant time spacing, in addition to generating the P and T waveforms on ECG. The results are compared numerically with the actual ECG. The work resulted in advances in oscillator models that can generate heart signals.