一类具有强Allee效应的捕食-食饵模型的共存性  

Coexistence for a predator-prey model with strong Allee effect

作　　者：罗碧梅 贾云锋[1] 娄烁烁 LUO Bi-mei;JIA Yun-feng;LOU Shuo-shuo(School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《云南大学学报（自然科学版）》2019年第1期13-17,共5页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11771262;61672021);陕西省自然科学基础研究计划(2018JM1020);中央高校基本科研业务费专项资金(GK201701001)

摘　　要：研究了一类具有强食饵Allee效应的捕食-食饵模型.首先,利用线性化方法证明了模型正平衡点的稳定性;其次,用最大值原理和Harnack不等式给出了相应的平衡态问题解的先验估计;最后,通过能量积分法和拓扑度理论分别得到了模型非常数正解的不存在性与存在性.研究结果表明:适当控制食饵的Allee效应,两物种可以共存.A predator-prey model with strong Allee effect of prey is considered. Firstly, by use of the linearization method, the stability of the positive equilibrium is proved;Then, a priori estimate of solutions of corresponding steady-state problem is given by the maximum principle and the Harnack inequality;Finally, the nonexistence and existence of non-constant positive solutions are established by the energy integration and the topological degree theory, respectively. The result shows that the predator and prey can coexist when the prey’s Allee effect is controlled reasonably.

关 键 词：捕食-食饵模型 强Allee效应 拓扑度理论 存在性 

分 类 号：O175.2[理学—数学]