具有Michaelis-Menten收获和避难所的捕食系统的分歧

The bifurcation of a predator-prey system with Michaelis-Menten type prey harvesting and refuge

在齐次Neumann条件下研究了一类具有扩散的带Michaelis-Menten收获项和避难所的捕食-食饵模型.首先利用稳定性理论证明了正常数平衡解的局部稳定性;其次利用最大值原理、Harnack不等式和能量积分的方法给出了正常数平衡解的先验估计和非常数正解的不存在性;再次由单特征值分歧理论得到了系统发自正常数平衡解处的解分支;最后利用Hopf分歧理论研究了在正常数平衡解处Hopf分歧存在的条件.

The bifurcation of a diffusive predator-prey models with Michaelis-Menten type prey harvesting and refuge is considered under homogeneous Neumann boundary condition. Firstly,the local stability of positive constant steady-state solution is obtained by using the theory of stability; secondly,by using the maximum principle,Harnack inequalities and the integral property,the priori estimates of positive steady-state solutions and the non-existence of the non-constant positive steady-state solutions are proved; the local bifurcation from the positive constant steady-state solutions is given by further applying simple eigenvalue bifurcation theory; finally,the positive constant steady-state solution where Hopf bifurcation occurs is investigated by using Hopf bifurcation theory.