具有非局部竞争的Holling-Tanner捕食模型的稳定性分析  

Stability Analysis of the Holling-Tanner Predation Model with Non-Local Competition

作　　者：杨尤伟 伍代勇 YANG Youwei;WU Daiyong(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2023年第4期24-28,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学基金(2108085MA10);安庆师范大学数理学院院级项目(Y201003034)。

摘　　要：非局部项代表食饵种群密度的空间加权平均,其描述了食饵之间的竞争不仅依赖于某一个位置的种群密度,而且还依赖于该位置附近的种群密度。本文构建了一类具有非局部食饵竞争的Holling-Tanner捕食模型,并探究了非局部食饵竞争模型的平衡点存在性。与此同时,在共存平衡点存在的条件下,给出了对于非局部食饵竞争模型的共存平衡点稳定性条件。此外,通过数值模拟对相关理论结果进行了验证和补充。结果表明,与局部食饵竞争相比,非局部食饵竞争会使共存平衡点失稳。The non-local term represents the spatially weighted average of the prey’s population density,which describes that the competition among prey depends on not only the population density at a certain location,but also the population densi-ty in the vicinity of that location.Therefore,this paper constructed a Holling-Tanner predation model with non-local prey com-petition was constructed,and explored the existence of the equilibrium points of the non-local prey competition model.Under the condition of the existence of the coexistence equilibrium point,we give the stability condition of the coexistence equilibri-um point for the non-local prey competition model.Relevant theoretical results are verified and supplemented by numerical simulations.The results show that compared with local prey competition,non-local prey competition destabilizes the coexis-tence equilibrium point.

关 键 词：捕食者-食饵模型 非局部食饵竞争 平衡点 稳定性 

分 类 号：O175[理学—数学]