= Piecewise linear relaxation-oscillator period
{title2=$T\sim\log[(1+\alpha)(1-\beta)/(-\alpha\beta)]$}
For $\epsilon\dot v=g(v)-w$, $\dot w=v$, let $g=-v$ below $\alpha$, $g=1-v$ above $\beta$, and join the endpoints by an increasing line, with $-1<\alpha<0<\beta<1$ and $\beta-\alpha<1$. The slow branches obey $\dot w=-w$ and $\dot w=1-w$ between $w_L=-\alpha$ and $w_R=1-\beta$. Their travel times are $\log[(1-\beta)/(-\alpha)]$ and $\log[(1+\alpha)/\beta]$. Fast horizontal jumps contribute vanishing time as $\epsilon\to0$, giving the displayed <relaxation oscillation> period.
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