Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2

Abstract

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