具有捕食者Allee效应的Leslie - Gower模型的动力学分析

研究了在Leslie - Gower模型中加入捕食者Allee效应后的模型动力学行为变化.研究表明:加入捕食者Allee效应后,模型的所有正解是一致有界的,唯一的正平衡点是全局渐近稳定的,但两个边界平衡点是不稳定的.Allee效应虽然不会改变正平衡点的稳定性,但其延长了正平衡点趋向稳定状态的时间,同时也改变了原点的性态,即Allee效应不利于系统的稳定性.

Dynamics of the Leslie-Gower model with Allee effect in predator

Dynamic behaviors of the Leslie - Gower model with Allee effect in predator are studied to show the influence of Allee effect.It is shown that positive solutions of this system are all uniformly bounded, and the only positive equilibrium of the system is globally asymptotically stable while the two boundary equilibrium points are all unstable with the Allee effect.The result indicates that Allee effect doesn't change the stability of the positive equilibrium but makes the system take a longer time to reach its steady - state solution, and it also changes the dynamic behaviors of the original point, which is to say that the Allee effect makes the system become unstable.