捕食率对一类食饵-捕食者动力学模型稳定性的影响  

Effects of Predation Rates on Dynamical Stability of a Prey-predator Model

作　　者：王成宇 申传胜 陈萌昭 徐王军 WANG Chengyu;SHEN Chuansheng;CHEN Mengshao;XU Wangjun(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2021年第1期84-91,共8页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11975025)。

摘　　要：在传统的食饵-捕食者模型中引入一个新的中间物种,该中间物种捕食原模型中的食饵,又被原捕食者所捕食,采用Logistic人口模型和Holling-I型功能响应函数给出这三个物种的动力学方程模型,解析得到该模型的平衡点以及它们的存在条件。利用雅可比矩阵和Routh-Hurwitz判据分析了平衡点的稳定性。数值模拟结果发现捕食率对捕食者自身的生存与灭绝具有十分重要的意义。In this paper,we incorporate an intermediate species into the traditional prey-predator model,where the intermediate species can hunt the original prey and may also be hunted by the original predator.We propose a dynamic equation model by using logistic law to describe the growth rates and with Holling-I functional response to describe three species preypredator relationship.The equilibrium points of the proposed model and their existence conditions are obtained.The dynamic stability of the equilibrium points is analyzed by using Jacobi matrix and the Routh-Hurwitz criteria.Numerical simulation results show that the predator’s predation rate is of great importance to the predator’s own survival and extinction.

关 键 词：食饵-捕食者模型 平衡点 稳定性 捕食率 

分 类 号：O175[理学—基础数学]