= Biased van der Pol relaxation period
{c}
{title2=$\mathcal T\sim k[3+(\lambda^2-1)\log((4-\lambda^2)/(1-\lambda^2))]$}
For $\ddot x+k(x^2-1)\dot x+x=\lambda$, with fixed $|\lambda|<1$ and $k\to\infty$, the Liénard coordinate $y=\dot x/k+x^3/3-x$ has fast horizontal jumps and slow motion on $y=x^3/3-x$. The slow time is $t/k$. Integrating $(x^2-1)dx/dT=\lambda-x$ along $[-2,-1]$ and $[2,1]$ gives the displayed <period>. The two jumps take negligible time at this scale. For fixed $\lambda>1$, the right attracting branch contains the stable <equilibrium> and the large relaxation cycle disappears.
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