具Allee效应和空间保护域的扩散捕食者-食饵系统分析  

Analysis of a Diffusive Predator-Prey System with Allee Effect and Spatial Protection

作　　者：王伟伟 赵治涛[1] Wang Weiwei;Zhao Zhitao(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,黑龙江哈尔滨150086

出　　处：《南开大学学报（自然科学版）》2021年第3期60-66,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(11201128);黑龙江省自然科学基金(LH2019A022)。

摘　　要：研究了一个具Allee效应和食饵空间保护域的扩散捕食者-食饵系统,给出系统解的全局存在性和耗散性,分析系统边界常值稳态解的存在性和稳定性,其中特别指出当捕食者分别是专食者和广食者时,常值稳态解稳定性的变化.最后利用庞加莱不等式和稳态分歧理论,建立系统非常值正稳态解的存在性与不存在性.A predator-prey system with Allee effect and spatial protection of prey is investigated. The global existence and dissipation of the solutions of the system are given, and the existence and stability of the boundary constant steady-state solutions of the system are analyzed. It is especially pointed out that the changes of the stability of the constant steady-state solutions when the predator is a specialist and a generalist respectively. Finally, by using Poincaré inequality and steady-state bifurcation theory, the existence and nonexistence of nonconstant positive steady-state solutions are established.

关 键 词：捕食者-食饵系统 ALLEE效应 空间保护域 稳态解 稳定性 

分 类 号：O29[理学—应用数学]