具有防御能力的Leslie-Gower捕食食饵模型的平衡态正解分析

Analysis of positive equilibrium solutions of Leslie-Gowerpredator-prey model with defensive ability

在Leslie-Gower捕食食饵模型中引入Monod-Haldane功能反应函数,研究齐次Dirichlet边界下食饵的防御能力对捕食系统平衡态正解的影响。利用极大值原理、上下解方法、分歧理论和稳定性理论等建立了平衡态正解的先验估计、存在的充要条件和局部稳定条件。结合数值模拟对平衡态正解进行定量分析。研究结果表明,只要食饵和捕食者的内禀生长率大于某个常数,就可产生共存模式。同时食饵防御能力会对捕食者产生抑制效应。特别地,当食饵具有较高生长率时,食饵抵御捕食者的能力更强。

Monod-Haldane functional response function is introduced into Leslie-Gower predator-prey model under the homogeneous Dirichlet boundary condition,the influence of the defensive ability of prey on the positive equilibrium solution of the predator-prey system is studied.A priori estimate,sufficient and necessary conditions for the existence and local stability of the positive equilibrium solution are established by using the maximum principle,the super and sub-solution method,bifurcation theory and stability theory.Combined with numerical simulation,the positive equilibrium solution is quantitatively analyzed.The research shows that as long as the intrinsic growth rate of prey and predator is greater than a certain constant,the coexistence mode can be generated.At the same time,the defense ability of prey has an inhibitory effect on the predator;especially when the prey has a higher growth rate,the ability of prey to resist the predator is stronger.