  To explain the phenomenon of bifurcation delay, which occurs in planar
systems of the form $\dot{x}=\epsilon f(x,z,\epsilon)$,
$\dot{z}=g(x,z,\epsilon)z$, where $f(x,0,0)>0$ and $g(x,0,0)$ changes sign at
least once on the $x$-axis, we use the Exchange Lemma in Geometric Singular
Perturbation Theory to track the limiting behavior of the solutions. Using the
trick of extending dimension to overcome the degeneracy at the turning point,
we show that the limiting attracting and repulsion points are given by the
well-known entry-exit function, and the maximum of $z$ on the trajectory is of
order $\exp(-1/\epsilon)$. Also we prove smoothness the return map up to
arbitrary finite order in $\epsilon$.
