The entry-exit function and geometric singular perturbation theory

Peter De Maesschalck, Stephen Schecter

For small $\epsilon >0$, the system $\dot{x}=\epsilon$, $\dot{z}=h(x,z,\epsilon )z$, with $h(x,0,0)<0$ for $x<0$ and $h(x,0,0)>0$ for $x>0$, admits solutions that approach the $x$-axis while $x<0$ and…