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

3.1.
 
ECG like wave generation with different fractional dynamical models 
The three different cases of fractional dynamics being present in the nonlinear term, 
the time delay coupling term and both the first two state equations are simulated now using 
the model (11). As expected, the FO coupled filtered VdP oscillator model behaves in a 
completely different manner as opposed to the integer order model in (10) as shown in Figure 
3-Figure 5. The time series generated by varying the fractional derivative operator gives a 
wide variety of ECG like waves relating various healthy and unhealthy physiological 
conditions. For all the three cases, mentioned earlier, it is observed that with a higher order 
(

) of fractional differential equation, the difference between two ECG beats are increased 
which may be an indication of a slow heart rate. Similarly small order of fractional 
differential equation represents more rapid heart rate. Thus it is clear that the FO models have 
higher capability of modelling the variation in different heart rates, by virtue of a single 
parameter i.e. the order of the fractional differential equation. Regarding periodicity of the 
ECG waves, FO coupled oscillator models are well behaved than the integer order 
counterpart. In Figure 3-Figure 5, it is observed that most of the ECG beats have equal 
magnitude, whereas the ECG beats from the integer order model in Figure 1 suffers from the 
presence of two beats with different amplitude. 
Figure 3 shows the ECG like time series using the FO coupled oscillator model (11) 
by considering the fractional dynamics to appear only in the first state equation, affecting the 
nonlinear cross-product term (case 11a). It is seen that except differential equation of 
order
0.7


, rest of the models having
0.8,1.2,1.4


are capable of producing ECG like 
waveform, at least the “QRS” complex of equal amplitude, excluding the “P” and “T” waves. 

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11
Also, for
0.8


, the “Q” and “S” wave amplitudes are almost equal which is rarely seen in 
real ECG signals.