EXISTENCE AND UNIQUENESS OF THE POSITIVE STEADY STATE SOLUTION FOR A LOTKA-VOLTERRA PREDATOR-PREY MO

• 作 者: Xianzhong ZENG Lingyu LIU Weiyuan XIE
• 机 构: School of Mathematics and Computing Science, Hunan University of Science and Technology,Xiangtan 411
• 出 处: 数学物理学报（英文版）
• 发表日期: 2020年6期
• 关键词: Lotka-Volterra predator-prey model crowding term critical value coexistence

This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation. We obtain a critical value λD1(Ω0), and demonstrate that the existence of the predator in (Ω)0 only depends on the relationship of the growth rate p of the predator and λD1(Ω0), not on the prey. Furthermore, when μ ＜ λD1(Ω0), we obtain the existence and uniqueness of its positive steady state solution, while when μ ≥ λD1(Ω0), the predator and the prey cannot coexist in (Ω)0. Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding region(Ω)0, which is different from that of the classical Lotka-Volterra predator-prey model.