一类具有毒素影响和Allee效应的捕食-被捕食模型的定性分析  

Qualitative Analysis of a Predator-Prey Model with Toxin and Allee Effect

作　　者：史明静 李泽妤[2] 赵艺 张蒙 SHI Mingjing;LI Zeyu;ZHAO Yi;ZHANG Meng(School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044;Canvard College, Beijing Technology and Business University, Beijing 101118)

机构地区：[1]北京建筑大学理学院,北京100044 [2]北京工商大学嘉华学院,北京101118

出　　处：《北京建筑大学学报》2021年第4期103-108,共6页Journal of Beijing University of Civil Engineering and Architecture

基　　金：国家自然科学基金项目(11701026)。

摘　　要：基于考虑环境中有毒物质对种群的影响,建立了一类食饵具有Allee效应的捕食-被捕食模型。分析了模型解的正性与有界性,利用常微分方程定性理论研究了平衡点的存在性及其局部稳定性,并通过构造相应的函数得到了极限环不存在的充分条件,以及模型一致持久的充分条件。最后,利用数值模拟验证了结论的正确性,还分析了Allee阈值与毒性系数对模型的影响,结果表明其影响是可控的。Considering the effect of toxic substances in the environment on the population,a predator-prey model with Allee effect is established.The positivity and boundedness of the solutions of the two-dimensional dynamical system are analyzed,as well as the existence and local stability of the equilibrium is studied by using the theory of the ordinary differential fundamental.Moreover,the nonexistence of limit cycle and the persistence of the model is obtained by constructing corresponding function.Finally,the correctness of the conclusion is verified by numerical simulation,and the influence of Allee threshold and toxicity coefficient on the model is analyzed.The results show that the influence is controllable.

关 键 词：毒素 ALLEE效应 捕食-被捕食 一致持久性 

分 类 号：O175.13[理学—数学]