一类具有Allee效应的偏害系统的稳定性分析  

Stability Analysis of a Kind of Amensalism System with Allee Effect

作　　者：石志高 SHI Zhi-gao(Teaching and Research Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, China)

机构地区：[1]福建江夏学院数理教研部,福建福州350108

出　　处：《中北大学学报（自然科学版）》2020年第5期394-396,404,共4页Journal of North University of China(Natural Science Edition)

基　　金：福建省中青年教师教育科研项目(JT180586)。

摘　　要：考虑一类具有Allee效应的偏害系统,首先对系统的平衡点性态进行了分析,其次对系统的持久性进行了验证,然后利用Dulac判定准则证明了系统在正平衡点附近不存在极限环和全局渐近稳定的结论,最后通过数值仿真解释了系统的Allee效应.A class of amensalism system with Allee effect was considered.Firstly,we analyzed the behavior of the equilibrium of the system,and then verified the persistence of the system.Then we used the Dulac criterion to prove that there was no limit cycle and global asymptotic stability near the positive equilibrium.Finally,we explained the Allee effect of the system by numerical simulation.

关 键 词：ALLEE效应 偏害系统 全局稳定 数值仿真 

分 类 号：O175.1[理学—数学]