疾病在食饵中进行传播的无差别捕食的捕食–食饵系统的定性分析

Qualitative Analysis of a Predator-Prey System with Undifferentiated Predation and Disease Is Spread in the Bait

研究一类疾病在食饵中进行传播的捕食–食饵系统,食饵受到密度制约,且捕食者进行不区分食饵是否感染疾病的无差别捕食。讨论了模型存在边界平衡点的条件,并通过计算系统的Jacobian矩阵,根据Routh-Hurwitz判据证明了系统的局部稳定性。利用Bendixson-Dulac判别法,证明极限系统不存在全部位于G内的闭轨线,从而得到极限系统的零解是全局稳定的;由极限系统理论,得到原系统的全局渐近稳定性。最后,讨论了正平衡点的存在性以及极限系统的极限环的存在性。

In this paper, a predator-prey system is studied for the propagation of a class of diseases in the prey. The prey is restricted by density, and the predator does not discriminate whether the food is infected or not. This paper discusses the condition of the boundary equilibrium points of the model, and proves the local stability of the system according to the Routh-Hurwitz criterion by the Jacobian matrix. Using Bendixson-Dulac criterion, the ultimate proof system does not exist all the closed orbits in G. Thus the zero solution of the limit system is global stable. The global asymptotic stability of the original system is obtained by the limit system theory. Finally, the existence of the positive equilibrium and the limit cycle of the limit system are discussed.