摘要
考虑一个具有联合收获和时滞的Lotka-Volterra竞争模型,其中一个物种受Allee效应影响,分析了该模型平衡点的局部以及全局稳定性.结果表明,依据不同的参数区域,两物种共存或出现竞争排斥,可通过调整模型的初始值或捕获努力量,使模型的解到达期望的状态,对于生物入侵防控及培育珍稀物种具有指导意义.讨论了当两时滞不同时为0时,模型出现分支的情形.模型存在一个临界时滞值,当时滞小于临界时滞值时,共存平衡点是局部渐近稳定的;当时滞等于临界时滞值时,Hopf分支出现.采用数值模拟说明了分析和结论 .
A Lotka-Volterra competition model was considered, in which both species had harvesting and were effected by time delay, and one species was subjected to Allee effect. The local and global stability of the equilibrium point of the model was analyzed. The results of the study showed that, according to different parameter areas, the two species either coexisted or competitively excluded each other. The solution of the model could reach the desired state by adjusting the initial value or the harvesting effort.This has a certain guiding significance for preventing and controlling biological invasion and breeding rare species. The research also discusses the bifurcation situation of the model when the two time delays were not equal to 0 at the same time. There existed a critical value of time delay, such that the equilibrium point was locally asymptotically stable when the delay was smaller than the critical value, and a Hopf bifurcation appeared when the delay was equal to the critical value. The numerical method was also used to verify the results of our analysis.
作者
邹温泉
李维德
ZOU Wen-quan;LI Wei-de(Center of Data Science,School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China)
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
2021年第6期798-810,共13页
Journal of Lanzhou University(Natural Sciences)
基金
国家重点研发计划项目(2018YFC0406606)。
