一类具有恐惧效应和同类相食的捕食者-食饵模型  

A predator-prey model with fear effect and cannibalism

作　　者：李博涵 刘俊利[1] 刘飞燕 LI Bohan;LIU Junli;LIU Feiyan(School of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《黑龙江大学自然科学学报》2025年第1期27-36,共10页Journal of Natural Science of Heilongjiang University

基　　金：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项目(2024JC-YBMS-001,2022JM-023)。

摘　　要：为了研究恐惧效应和同类相食对捕食者-食饵模型的影响,在具有恐惧效应且功能反应函数为Holling-Ⅱ型的模型中加入了捕食者同类相食,证明了模型解的非负有界性,给出了平衡点存在的充分条件。运用线性化方法和构造Dulac函数,讨论了平衡点的全局稳定性,研究了边界平衡点处的鞍结点分支和正平衡点处的Hopf分支。研究表明,较高的恐惧水平可以通过排除周期解的存在来确保捕食者-食饵模型的稳定,而较低的恐惧水平可以通过亚临界Hopf分支产生多个极限环,进而达到双稳定状态。与忽略捕食者同类相食的具有恐惧效应的捕食者-食饵模型相比,该模型表明更高的同类相食率更有利于模型的稳定。In order to study the effects of fear effect and cannibalism on a predator-prey model,predator cannibalism was added to the model,which incorporated fear effect and a Holling-Ⅱtype functional response function.The non-negativity and boundedness of the solutions of the model was proved,sufficient conditions for the existence of equilibria were given.By the linearization and the Dulac function,the global stability of the equilibrium was proved,the saddle-node bifurcation at the boundary equilibrium and the Hopf bifurcation at the positive equilibrium were studied.It shows that higher levels of fear can ensure the stability of predator-prey model by eliminating the existence of periodic solutions,while lower levels of fear can induce multiple limit cycles through subcritical Hopf bifurcation,leading to bi-stability state.Compared to the predator-prey models with fear effect but ignore predator cannibalism,the model implies that a higher cannibalism rate is more conducive to the stability of the model.

关 键 词：恐惧效应 同类相食 DULAC函数 Holling-Ⅱ型功能反应函数 鞍结点分支 HOPF分支 

分 类 号：O175.1[理学—数学]