English

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 22 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 P\mathcal{P} such that for each zPz\in \mathcal{P}, the ω\omega-limit set ω(z)\omega(z) 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}
}