具有食饵选择的食物链模型的定性分析

生态学研究发现，多种食饵选择对捕食者-食饵系统的稳定性、持久性等方面有着重要的影响。处于食物链中间层的种群，既是顶层捕食者的食饵，同时又是捕食者，因此中间捕食者的种群数量变化，对整个生态系统有着不可忽略的影响。假设中间捕食者具有其他可供选择的食饵，建立了一个由顶级捕食者、中间捕食者和食饵所构成的三维食物链系统，并对此系统展开动力学分析，推导出系统各个平衡点的存在性和稳定性条件。对Hopf分支的存在性条件进行了深入的分析，并以食饵选择参数为分支参数，对可能出现的Hopf分支情况进行了数值模拟。结合理论和数值结果，分析食饵选择性对食物链系统的稳定性产生的影响。

Qualitative analysis of a food chain model with alternative prey

Studies in ecology show that alternative prey has important effects on predator-prey system in the aspects of system stability, species persistence, etc. For species at the intermediate level of a food chain, they are prey of top predators, while predating the bottom prey at the same time. Therefore, the effect of changes in intermediate predators' population on the system cannot be ignored. We set up a three-dimensional food chain model composed of top predator, intermediate predator and prey, assuming that the intermediate predator had alternative choice of prey. The existence and stability of the equilibria were derived through dynamical study of the system. The existence of Hopf bifurcation was explored in depth. The numerical simulations used the prey choice parameter as the bifurcation variable to study the possible Hopf bifurcations. The effect of alternative prey on the stability of the food chain system was derived through the theoretical and numerical results.