GENERIC POINCARE-BENDIXSON THEOREM FOR SINGULARLY PERTURBED MONOTONE SYSTEMS WITH RESPECT TO CONES OF RANK-2

被引：0
|
作者：
Niu, Lin [1 ,2 ]
Xie, Xizhuang [2 ,3 ]
机构：
[1] Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China
[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[3] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 10期
关键词：
Monotone systems with respect to 2-cones; regular perturbation; singular perturbation; generic Poincare-Bendixson Theorem; DIFFERENTIAL-EQUATIONS; STRONGLY MONOTONE; ORBITAL STABILITY; CONVERGENCE; EXISTENCE; BEHAVIOR; CYCLES;
D O I：
10.1090/proc/16515
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the singularly perturbed monotone systems with respect to cones of rank 2 and obtain the so called Generic Poincare'-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 ?-limit set ?(z) that contains no equilibrium points is a closed orbit.
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页码：4199 / 4212
页数：14
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