  We investigate the singularly perturbed monotone systems with respect to
cones of rank $2$ and obtain the so called Generic Poincar\'{e}-Bendixson
theorem for such perturbed systems, that is, for a bounded positively invariant
set, there exists an open and dense subset $\mathcal{P}$ such that for each
$z\in \mathcal{P}$, the $\omega$-limit set $\omega(z)$ that contains no
equilibrium points is a closed orbit.
