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

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.