具有合作行为且捕食者患病的生态流行病模型分析  

Analysis of an Eco-Epidemiological Model with Cooperative Behavior and Predator Morbidity

作　　者：张攀 王稳地[1] 向茜 ZHANG Pan;WANG Wen-di;XIANG Qian(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院

出　　处：《西南师范大学学报（自然科学版）》2019年第5期7-12,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11571284)

摘　　要：研究了一类捕食者患病的捕食-食饵模型,且考虑捕食者种群存在合作捕食行为.首先讨论了无病子模型的动力学性质,通过构造合适的Lyapunov函数,证明了边界平衡点的全局稳定性,利用Dulac函数讨论了仅一个正平衡点时的全局稳定性以及Hopf分支产生的情况.其次讨论了有病系统中三者共存的平衡点的情况,利用Hurwitz判据得到共存平衡点的稳定条件.In this paper, a predator-prey model with predator disease has been studied, and the cooperative predator behavior been considered. Firstly, the dynamic properties of the disease-free sub-model have been discussed. By constructing a suitable Lyapunov function, the global stability of the boundary equilibrium point has been proved. By using Dulac function, only one positive equilibrium point has been discussed. The global stability of Hopf bifurcation has been discussed. Secondly, the equilibrium point of the three coexistence in the diseased system has been discussed. The stability condition of the coexistence equilibrium point has been obtained by using Hurwitz criterion.

关 键 词：LYAPUNOV函数 DULAC函数 全局稳定性 HOPF分支 

分 类 号：O175[理学—数学]