一类带有Crowley-Martin反应函数的捕食-食饵模型的定性分析

摘要

讨论了一类带有Crowley-Martin 反应函数的具有一个食饵和两个捕食者的捕食-食饵模型正解的存在性和持久性。首先利用空间分解和隐函数定理研究了系统的二重分歧，得到了正平衡解存在的充分条件。其次给出了系统正平衡解不存在的充分条件。最后讨论了抛物系统正解的渐近行为，利用比较原理给出了系统持久和灭绝的充分条件。%The existence and permanence of the positive solutions for a one-prey and two-predators model with Crowley-Martin type functional response are considered.First,the bifurcation from a double eigen-value for system is discussed by virtue of the space decomposition and the implicit function theorem,and the sufficient conditions for the existence of the positive steady-state solutions are obtained.Moreover,the sufficient conditions for the non-existence of the positive steady-state solutions are given.Finally,asymp-totic behavior of the positive solutions of the parabolic system is investigated,and the sufficient conditions for extinction and permanence of the parabolic system are given by using the comparison theorem.