一类具有时滞的宿主-寄生虫交互模型的分支方向、稳定性和周期的研究

Analysis of the Bifurcation Direction,Statibility and Period of a Host-parasite Interaction Model with Delay

考虑了一类具有细胞内时滞的宿主-寄生虫交互模型.由于时滞会导致Hopf分支的发生,在已有的研究结果基础上,利用规范型理论和中心流形的方法,得到了决定分支方向、稳定性和周期的表达式.最后,利用数值计算验证了理论结果.

Many diseases is caused by parasites invaded the hosts. Thus,the study of host-parasite interaction is an interesting problem. In this paper,the bifurcation direction,statibility and period of a host-parasite model with intracellular delay is investigated. By use of the normal form theorem and center manifold argument,we obtain the formula which determined the direction,stability and period of bifurcation periodic solution. Then,we give an example to verify our theoretical results.