%0 Journal Article
%T 一类两种群都染病的捕食—食饵模型分析<br>A Predator-Prey Mathematical Model with Both the Populations Affected by Diseases
%A 范城玮
%A 刘贤宁&lt
%A br&gt
%A FAN Cheng-wei
%A LIU Xian-ning
%J 西南大学学报(自然科学版)
%D 2018
%R 10.13718/j.cnki.xdzk.2018.05.015
%X 建立了一类两种群都染病的捕食—食饵模型，证明了解的正性和最终有界性；利用Hurwitz判据，得到了边界平衡点局部渐近稳定的充要条件并发现系统的正平衡点是不稳定的；通过构造适当的Lyapunov函数，给出了边界平衡点全局稳定的充分条件.<br>In this paper, a predator-prey mathematical model with both the populations affected by diseases is proposed. The positivity and ultimate boundedness of the solution is proved. The necessary and sufficient conditions for the locally asymptotic stability of the boundary equilibrium are established by using Hurwitz criterion. And the positive equilibrium point is proved to be always unstable. The sufficient conditions for the globally asymptotic stability of the boundary equilibrium are given by constructing some reasonable Lyapunov functions
%K 捕食—食饵模型
%K Hurwitz判据
%K Lyapunov函数
%K 全局渐近稳定性&lt
%K br&gt
%K prey-predator model
%K Hurwitz criterion
%K Lyapunov function
%K globally asymptotic stability
%U http://xbgjxt.swu.edu.cn/jsuns/html/jsuns/2018/5/201805015.htm