Van der Pol Oscillator - Demo 2

Relaxation Oscillations

For large values of b the oscillations take on the form of relaxation oscillations. We can try to verify the shape of the orbit in phase space using e.g. b=10. (Because of the rapid time dependence over part of the cycle, the numerical integration must use a small time step. If the dynamics is too slow on your computer, reduce b and increase dt.

Notice the two different time scales for the different parts of the orbits - a slow evolution and then a rapid jump.

This is also shown by looking directly at X(t):

The power spectrum of X(t) shows many harmonics with strength comparable to the fundamental, and the frequency of the oscillation is changed significantly from the small amplitude value.

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Last modified Saturday, November 27, 1999
Michael Cross