Fractional Dynamical Model for the Generation of ecg like Signals from Filtered Coupled Van-der Pol Oscillators

Figure
 
8:
 
Phase
 
space
 
representation
 
of
 
oscillator
 
waves
 
with
 
fractional
 
dynamics
 
in
 
second
 
state
 
variable
 
(11b).
 
3.3.
 
Clinical analogy with healthy and diseased ECG patterns 
It has been seen in earlier sections that due to the introduction of the fractional 
dynamics in various state equations in different combination and the respective values of the 
fractional orders of the differential equations give rise to ECG waves with high and low heart 
rate. In ECG literatures, this typical behaviour of very low hear-rate (<60/min) and very high 
heart-rate (>100/min) are known as 
sinus bradycardia 
and 
sinus tachycardia
respectively 
[53]. Thus the proposed fractional dynamical modes can easily capture such wide variation in 
the heart rate with the same generalized template (11) by only suitable modification of the 
order of the differential equations.
The waveforms generated with the integer order two-oscillator model (10) with equal 
time delays in coupling is similar to the case of 
premature ventricular contraction 
where 
between two normal R peaks a sudden occurrence of distorted “R”-peak can be observed 
[53]. This typical phenomenon is generally originated from the ventricular muscle. In such a 
diseased condition generally the “P”-waves are not seen. 
The absence of the P wave for the above mentioned models can be compared to the 
case of 
junctional rhythm
of ECG dynamics. In this particular case, often the “P” wave gets 

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superimposed with the “QRS” complex and not seen separately [53]. The source of this