一类具有时滞的生态一流行病系统的稳定性和Hopf分支

Stability and Hopf Bifurcation of an Eco-epidemiological System with Delay

讨论一类食饵染病的时滞捕食一被捕食者模型，通过分析特征方程，得到正平衡点局部稳定和Hopf分支存在的条件．同时，应用中一tl,流形定理和规范型理论研究正平衡点处Hopf分支方向和分支周期解的稳定性．最后，通过数值模拟对理论结果进行了说明．

A predator-prey system with time delay and disease in the prey is investigated. By analy- zing the corresponding characteristic equation, the local stability of a positive equilibrium is inves- tigated. The existence of Hopf bifurcations is established. Formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.