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arXiv · 2110.11783

Generic Poincar\'{e}-Bendixson Theorem for singularly perturbed monotone systems with respect to cones of rank-$2$

Lin Niu·Xizhuang Xie
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Abstract

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.

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Lin Niu, Xizhuang Xie. 2021-10-22. Generic Poincar\'{e}-Bendixson Theorem for singularly perturbed monotone systems with respect to cones of rank-$2$. https://arxiv.org/abs/2110.11783

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