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

Niu, Lin; Xie, Xizhuang

doi:10.1090/proc/16515

Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-$2$
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by Lin Niu and Xizhuang Xie;

Proc. Amer. Math. Soc. 151 (2023), 4199-4212

DOI: https://doi.org/10.1090/proc/16515

Published electronically: July 21, 2023

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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 Poincaré-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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