具有强Allee效应Rosenzweig-MacArthur时滞模型的问题研究
Research on Rosenzweig-MacArthur Delay Model with Strong Allee Effect
摘要: 本文提出了一个具有强Allee效应和双曲正切函数功能反应的Rosenzweig-MacArthur捕食者–被捕食时滞模型。讨论模型中正解的存在性，利用下一代矩阵法得到基本再生数，并在Hurwitz判据的条件下重点分析可行平衡点的稳定性。并在特定条件下，给出了平衡点局部稳定的条件和Hopf分支的存在性条件。
Abstract:
A Rosenzweig-MacArthur predator-prey delay model with strong Allee effect and hyperbolic tan-gent function is proposed. The existence of the positive solution in the model is discussed, and the basic regeneration number is obtained by using the next generation matrix method. The stability of the feasible equilibrium point is analyzed mainly under the condition of Hurwitz criterion. The local stability of equilibrium point and the existence of Hopf branch are given under certain conditions.
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