一类具有Allee效应和同类相食的捕食者-食饵模型  

A class of predator-prey models with Allee effect and cannibalism

作　　者：李博涵 刘俊利[1,2] LI Bohan;LIU Junli(School of Science,Xi an Polytechnic University,Xi an 710048,China;Xi an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms,Xi an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048 [2]西安大数据分析及算法国际科技合作基地,西安710048

出　　处：《扬州大学学报(自然科学版)》2025年第2期70-78,共9页Journal of Yangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11801431);陕西省杰出人才资助项目(10701000506);陕西省自然科学基础研究计划资助项目(2024JC-YBMS-001)。

摘　　要：为探讨Allee效应和同类相食对捕食者-食饵模型的影响,在包含Allee效应和比率依赖型功能反应函数模型中引入同类相食,分析模型的动力学特性,讨论平衡点的存在性和稳定性,研究正平衡点处的鞍-结点分支、Hopf分支以及余维2的Bogdanov-Takens分支。结果表明:Allee效应使模型产生更复杂的动力学行为,并引发更高维的分支;较低的同类相食率有利于维持模型的稳定性;与仅含Allee效应或同类相食的捕食者-食饵模型相比,两种生物学机制共存情况下,同类相食能够在一定程度上缓解Allee效应所导致的灭绝风险,并且Allee效应通过限制低密度种群中的同类相食行为,提高了种群的生存概率,增加了模型的稳定性。To investigate the effects of Allee effect and cannibalism on predator-prey model,cannibalism is introduced into the model containing Allee effect and ratio-dependent functional response function,and the dynamical properties of the model are analyzed to discuss the existence and stability of equilibrium points.The saddle-node bifurcation,Hopf bifurcation,and the codimension-2 Bogdanov-Takens bifurcation at the positive equilibrium are studied.The results show that the Allee effect makes the model produce more complex dynamical behavior and leads to higher-dimensional bifurcations.Low cannibalism rate is beneficial to maintain the stability of the model.Compared with predator-prey models containing only the Allee effect or cannibalism,the coexistence of both mechanisms allows cannibalism to mitigate the extinction risk caused by the Allee effect to a certain extent.Moreover,the Allee effect restricts can improve the survival probability of the population and increase the stability of the model by limiting cannibalism behavior in low-density populations.

关 键 词：ALLEE效应 同类相食 鞍-结点分支 HOPF分支 Bogdanov-Takens分支 

分 类 号：O175.1[理学—数学]