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

2021/10/22 by Niu, Lin, Xie, Xizhuang
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.11783

Abstract

We investigate the singularly perturbed monotone systems with respect to cones of rank 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 such that for each z∈ P, the ω-limit set ω(z) that contains no equilibrium points is a closed orbit.

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