具协作狩猎和恐惧效应的扩散捕食者-食饵系统分析

Analysis of a diffusive predator-prey system with hunting cooperation and fear effect

捕食者的协作狩猎和对食饵产生的恐惧效应是捕食者-食饵系统研究中的两个重要问题。主要考虑在具协作狩猎和恐惧效应联合作用下一类扩散捕食者-食饵系统的动力学行为。基于上下解方法和抛物方程的比较定理,给出系统解的全局存在性和耗散性。利用椭圆算子主特征值理论,分析系统常值稳态解的存在性和局部稳定性,并给出Hopf分支的存在性;通过数值模拟验证了所得理论结果。

Hunting cooperation and fear effect are two important problems in the study of predator-prey systems.The dynamic behavior of a diffusive predator-prey system with hunting cooperation and fear effect is considered.Based on the method of upper and lower solutions and the comparison theorem of parabolic equation,the global existence and dissipativity of solutions of the system are given.By using the principal eigenvalue theory of elliptic operators,the existence and local stability of the steady-state solution of the system are analyzed,and the existence of Hopf bifurcation is given.The theoretical results are verified by numerical simulations.