一类具有非局部项的捕食食饵模型的动力学分析  

Dynamic Analysis of a Predator-Prey Model with Non-local Term

作　　者：张国颖 彭亚红 ZHANG Guoying;PENG Yahong(College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《东华大学学报（自然科学版）》2020年第5期819-827,共9页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金资助项目(11571227)。

摘　　要：在一类捕食食饵模型中引入非局部项,采用线性化和微分方程定性理论的方法,研究非局部项对正平衡点稳定性的影响,并给出模型发生图灵分支的条件。研究表明,在拉普拉斯函数的影响下,非局部项会使正平衡点处的稳定区域消失,且当参数满足一定条件时,模型会出现图灵分支。数值分析也例证了理论结果。The non-local term is introduced into a predator-prey model.By means of linearization and qualitative theory of differential equations,the influence of non-local term on the stability of positive equilibrium is studied.And the conditions of Turing bifurcation is given.Under the influence of the Laplace function,the non-local term will make the stable region at the positive equilibrium point disappear,and when the parameter satisfies certain conditions,the Turing bifurcation will appear.The numerical simulations also illustrates the theoretical results.

关 键 词：捕食食饵模型 非局部竞争 霍普分支 图灵分支 

分 类 号：O175.26[理学—数学]