具Allee效应的种群入侵数学模型

Properties of the species invasion model with Allee effect

借助带自由边界的反应扩散方程,建立具有Allee效应的种群入侵数学模型,描述入侵种群动态过程,探究该数学模型全局解的存在惟一性,同时对解的长时间性质进行研究,得到了入侵种群在新环境中扩张和灭绝的相应条件,揭示了种群因初始生存区域小或自身扩张能力差而导致灭绝的可能性,并利用MATLAB软件对所得结论进行了数值验证,为生态保护和有害种群入侵的防控提供了理论参考。

Based on the reaction diffusion equation with free boundary,the mathematical model of species invasion with Allee effect is established,the dynamic process of the invasive species is described,and the existence and uniqueness of the global solution of the model are explored.Focusing on the nature of the long-term solution,the corresponding conditions of the spreading or vanishing of the invasive species in the new environment are obtained,we have proved the conclusion that the possibility the specie will be vanish due to the small initial survival area or poor self-spreading ability,and verified our analytical findings numerically with MATLAB software.These results provide a theoretical basis for the prevention and control of ecological protection and harmful species invasion.