Van der Pol oscillator - Demonstrations

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The Van der Pol oscillator is described by the equations

d2x/dt2 - b (1 - x2) dx/dt + x = a cos(ct)

In autonomous form with X = x, Y = dx/dt, Z =c t:

dX/dt = Y
dY/dt = b(1 - X2)Y - X + a cos(Z)
dZ/dt = c

The parameters of the applet are a the strength of the driving, b the coefficient of the negative linear damping, and c the frequency of the external driving.


  1. Demonstration 1 - Small amplitude oscillations
  2. Demonstration 2 - Relaxation oscillations
  3. Demonstration 3 - Quasiperiodic motion
  4. Demonstration 4 - Frequency Locking

[First Demonstration] [Outline]
Last modified Saturday, January 10, 1998
Michael Cross

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