具有交叉扩散项与修正Leslie-Gower反应项的捕食-食饵模型的共存解

Coexisting Solutions of a Predator Prey Model with Cross Diffusion Terms and Modified Leslie-Gower Reaction Terms

为了研究一类具有交叉扩散项与修正Leslie-Gower反应项的捕食-食饵模型在Dirichlet边界条件下平衡态解的共存性,文中利用非线性理论给出了系统的平凡解与半平凡解的稳定性结论,利用最大值原理阐明了捕食-食饵模型共存态解的先验估计,利用Leray-Schauder度理论及不动点指标理论证明了共存态解存在的充分条件,利用数值模拟实现了一维方程的平衡态解的可视化。研究结果表明:具有交叉扩散项与修正Leslie-Gower反应项的捕食-食饵模型中的参数满足相应的数值时,系统中的两种生物可以共存。

In order to study the co existence of equilibrium solutions of a class of predator prey model with cross diffusion terms and modified Leslie-Gower reaction terms under Dirichlet boundary conditions,the paper provides a conclusion on the stability of trivial and semi trivial solutions of the system by using nonlinear theory and clarifies the prior estimation of coexistence solutions of the predator prey model by using the maximum principle.By using Leray Schauder degree theory and the fixed point index theory,the sufficient conditions for the existence of coexistence state solutions are proved,and the visualization of the equilibrium state solutions of one dimensional equations is realized by numerical simulation.The results show that when the parameters of the predator prey model with the cross diffusion term and the modified Leslie-Gower reaction term meet the corresponding values,two species in the system can coexist.