Global dynamics of 3D cooperative Lotka-Volterra system with the identical intrinsic growth rate

被引：0
|
作者：
Liang, Fengli [1 ]
Jiang, Jifa [2 ]
Zhang, Xiang [3 ,4 ]
机构：
[1] Anhui Normal Univ, Sch Math & Stat, Wuhu 241000, Peoples R China
[2] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China
[3] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China
[4] Shanghai Jiao Tong Univ, CAM Shanghai, Shanghai 200240, Peoples R China
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2024年 / 191卷
基金：
中国国家自然科学基金; 国家重点研发计划;
关键词：
Cooperative Lotka-Volterra system; Identical intrinsic growth rate; Global dynamics; Poincare compactification; DIFFERENTIAL-EQUATIONS; BEHAVIOR;
D O I：
10.1016/j.bulsci.2023.103382
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we complete the classification on global topological structures of the three-dimensional cooperative Lotka-Volterra system with the identical intrinsic growth rate inside the Poincare compactification of the positive octant of R3. Precisely, with the help of the replicator equations it is proved that this kind of system can have exactly 8 topologically different phase portraits. As a consequence, we obtain the necessary and sufficient conditions for the system to be bounded in the positive octant. (c) 2024 Elsevier Masson SAS. All rights reserved.
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页数：26
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