带有M-H反应项的捕食-食饵系统的分歧解

Bifurcation solutions for the predator-prey model with M-H functional response

目的在Dirichlet边界条件下研究一类带有Monod-Haldane反应项的捕食-食饵模型的动力学行为。方法利用椭圆型方程的极值原理和上下解方法给出了正解的先验估计,再结合局部分歧理论及稳定性理论对模型进行讨论。结果给出系统分歧解存在和稳定的充分条件。结论在一定条件下,具有相互制约关系的捕食者和食饵是可以共存的。

Purposes—The dynamic behavior of a predator-prey model with Monod-Haldane functional response is studied under Dirichlet boundary conditions.Methods—A priori estimates of positive solutions is given by using the extremum principle and upper-lower solutions method of elliptic equations,and then the model is discussed by combining the local bifurcation theory and stability theory.Result—Sufficient conditions for the existence and stability of bifurcation solutions are obtained.Conclusion—Under certain conditions,the predators and prey with mutual restriction can coexist.