避难所对食物链模型动力学行为的影响  

The influence of refuge on the dynamic behavior of food chain model

作　　者：苏茹燕 杨文生[1,2,3] SU Ruyan;YANG Wensheng(School of Mathematics and Statistics,Fujian Normal University;Fujian Key Laboratory of Mathematical Analysis and Applications;FJKLMAA and Center for Applied Mathematics of Fujian province(FJNU),350117,Fuzhou,Fujian,PRC)

机构地区：[1]福建师范大学数学与统计学院 [2]福建省分析数学及应用重点实验室 [3]福建省应用数学中心(福建师范大学),福建省福州市350117

出　　处：《曲阜师范大学学报（自然科学版）》2022年第1期19-26,共8页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11672074);福建省自然科学基金(2018J01655)。

摘　　要：文章研究了顶层捕食者对中层捕食者的食饵具有保护作用的食物链模型.利用线性稳定性理论讨论平衡点的局部渐近稳定性.通过构造合适的Lyapunov函数,证明在分别满足一定条件下,两个边界平衡点和正平衡点是全局渐近稳定的.最后通过数值模拟验证结论的可行性,并举例说明保护力度适当的避难所可以增加猎物的数量.当3个物种共存时,随着避难系数的增大,食饵的数量增加,且避难系数的变化对食饵数量的影响较大,对顶层捕食者数量的影响较小,对中层捕食者最终的数量没有影响.A food chain model in which the top predator has a protective effect on the prey of the middle predator is studied in this paper.By using the linear stability theory,the local asymptotic stability of the equilibrium point is discussed.By constructing appropriate Lyapunov functions,it is proved that the two boundary equilibrium points and the positive equilibrium points are globally asymptotically stable under certain conditions.Finally,the feasibility of the conclusions through numerical simulations is verified and some examples are given to illustrate that shelters with adequate protection can increase the number of prey.When the three species coexist,as the refuge coefficient increases,the number of prey increases.The change of refuge coefficient has greater impact on the number of prey and smaller impact on the number of top predators,and has no impact on the final number of middle predators.

关 键 词：避难 局部稳定性 全局稳定性 LYAPUNOV函数 

分 类 号：O175.1[理学—数学]