两种群捕食者-食饵模型解的整体性态

Global behavior of solutions to a two species predator-prey model

讨论了两种群捕食者-食饵模型解的整体性态。首先,讨论该模型解的整体存在性和一致有界性;其次,运用线性化方法得出该两种群模型的正平衡点和平凡平衡点均是无条件不稳定的,只有半平凡平衡点是局部渐近稳定的;最后,运用Lyapunov函数法得出该食物链模型的半平凡平衡点是全局渐近稳定的。

The global behavior of solutions to a two species predator-prey model is considered.Firstly,the global existence and uniform boundedness of solutions for this model are discussed.Then,using the linearization,we have learned that the positive equilibrium point and the ordinary equilibrium point is unconditionally instabilized,and that the semi-ordinary equilibrium point of the two species model is locally stabilized.Finally,using the Lyapunov function,we have got the result that the semi-ordinary equilibrium point for the food chain model is globally stabilized.