## van der Pol Oscillator on the phase plane

The 2nd order ODE for van der Pol oscillator
\(\ddot{x}+(x^2-1)\dot{x}+x=0\) is written as a system
of first order ODEs
\begin{equation}
\dot{x} = y +x-\frac{x^3}{3},\qquad
\dot{y} = -x.
\end{equation}
Notice the unusual choice of the variable \(y=\dot{x}-x+x^3/3\), which is more convenient
to show the existence of the periodic solution (call limit cycle) than the conventional
one \(y=\dot{x}\). You can **click your mouse on the plane** to see how the points converge to the periodic solution.