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3 Fundamentals of the Formation of Biosignals

Fig. 3.18: Modified Van der Pol oscillator according to Grudzinski and Zebrowski [23] according to

Equation 3.25 to describe the action potential of a vibration-generating nerve cell or a whole bundle

of similar nerve cells such as the SA or AV node.

time units

Voltage U / mV

Fig. 3.19: Action potential x(t) to the modified Van der Pol oscillator after [23] in Figure 3.18 with

parameters v1 = 1, v2 = −1, d = 3, e = 6 and α = 3.

since these equations for a = b = 0 describe the Van-der-Pol oscillator as a special

case. Such an oscillator can generate an oscillation without external excitation, which

simulates the potential of a nerve cell in generating oscillations. In the general case,

however, instead of the parameters a and b the original Van der Pol oscillator can be

extended in other ways to describe important properties of the action potential and

to influence the frequency and oscillation stability in a simpler way without changing

the signal form significantly [23]. This led to the modified equation:

­x + α(x −v1)(x −v2)^_x + x(x + d)(x + e)/ed = 0 ,

d, e, α > 0 .

(3.25)

The corresponding model is shown in Figure 3.18. This can be used to describe de facto

not only the action potential of a single nerve cell, but also that of a whole cluster

of similar nerve cells, such as in the sinus node. The corresponding action potential

shows Figure 3.19.