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## Relaxation Oscillator

Professor Strogatz Cornell course video lectures on “Nonlinear Dynamics and Chaos” are now online. This post pays homage to lecture 10 on analysis of the  Van der Pol equaltion:

$\ddot{x}+x+\mu \dot{x}(x^2-1)=0$

In the following the case for $\mu =2,\mu =10$ and the examination of the $\mu >>1$. It nicely illustrates the two time scales referred to, the slow then fast parts of the oscillation.

The phase portrait is the $x, y$ plane where $y$ is the the Lienard transformed and rescaled version of the equation.

So the system is:
$\dot{x}=\mu(y-(x^3/3-x))$
$\dot{y}=-x/\mu$