一类具有非单调生长率的捕食-食饵系统的动力学

Dynamics research in a predator-prey system with a nonlinear growth rate

研究了齐次Dirichlet边界条件下一类捕食-食饵系统的动力学,其中捕食者种群具有非单调生长率1/(1+ev)。利用隐函数定理,分歧理论和摄动技巧,得到了系统正平衡态的存在性,唯一性和稳定性,并通过数值模拟补充验证了相应的理论结果。

The paper is concerned with a predator-prey diffusive dynamics subject to homogeneous Dirichlet boundary conditions,where the predator population reproduces by the nonlinear function 1 /（ 1 ＋ ev）. Existence and uniqueness of coexistence states for the predator-prey system are investigated. M oreover,some asymptotic behaviors of time-dependent solutions are shown and some numerical simulations are done to complement the analytical results. The main tools used here include the implicit function theorem,the bifurcation theory and the perturbation technique.