# Van der Pol oscillator - Demonstrations

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The Van der Pol oscillator is described by the equations

d^{2}x/dt^{2} - b (1 - x^{2}) 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 - X^{2})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.
### Demonstrations

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

[First Demonstration]
[Outline]

Last modified Saturday, January 10, 1998

Michael Cross

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