Generic Poincar\'{e}-Bendixson Theorem for singularly perturbed monotone systems with respect to cones of rank-$2$
Dynamical Systems
2021-10-25 v1
Abstract
We investigate the singularly perturbed monotone systems with respect to cones of rank 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 such that for each , the -limit set that contains no equilibrium points is a closed orbit.
Keywords
Cite
@article{arxiv.2110.11783,
title = {Generic Poincar\'{e}-Bendixson Theorem for singularly perturbed monotone systems with respect to cones of rank-$2$},
author = {Lin Niu and Xizhuang Xie},
journal= {arXiv preprint arXiv:2110.11783},
year = {2021}
}