一类具有捕食者与食饵依赖功能性反应的种群模型的全局稳定性  

Global Stability for A Population Model with Predator-Prey-Dependent Functional Response

作　　者：杨文生 郑艳红 YANG Wen-sheng;ZHENG Yan-hong(College of Mathematics and Informatics,Fujian Normal University,Fuzhou,Fujian 350117 China;Fujian Key Laboratory of Mathematical Analysis and Applications,Fuzhou,Fujian 350117 China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117 [2]福建省分析数学及应用重点实验室,福建福州350117

出　　处：《生物数学学报》2020年第1期9-14,共6页Journal of Biomathematics

基　　金：supported by National Natural Science Foundation of China(11672074);the Natural Science Foundation of Fujian Province(2018J01655)

摘　　要：本文研究了一类具有Neumann边界条件的捕食者与食饵依赖模型.通过构造新的Lyapunov函数,得到了保证系统的唯一正平衡点是全局渐近稳定的充分条件.该充分条件比前人得到的条件更弱,更简洁.所得结论表明构造一个适当的Lyapunov函数对证明全局渐近稳定性是至关重要的.A predator-prey-dependent model with reaction-diffusion and Neumann boundary conditions is reconsidered in this paper.By constructing a new Lyapunov function,sufficient condition which ensures the global asymptotical stability of the unique positive equilibrium of the system is obtained.It is shown that our condition is weaker and simpler than the earlier one given in earlier paper.Therefore,constructing a suitable Lyapunov function is crucial to prove global asymptotic stability result.

关 键 词：捕食者与食饵依赖功能性反应 反应扩散 LYAPUNOV函数 全局渐近稳定性 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]