Allee效应对单种群模型动力学行为影响研究

The influence of Allee Effect to the Single Species Ecosystem

提出具有Allee效应的抽象的单种群模型,证得如果原系统有唯一的全局稳定的正平衡点,则具有Allee效应的单种群模型仍然具有唯一的全局稳定的正平衡点.Allee效应并不改变种群的平衡位置和稳定性;其后,针对具有Allee效应的对数种群模型,食物有限的单种群模型,Ayala型单种群模型分别进行了数值模拟,数值模拟表明随着Allee效应增大,系统的解需要更久的时间才能趋于正平衡点,从这一角度讲,Allee效应不利于系统的稳定,种群在受到外界干扰时,可能种群密度更容易出现剧烈波动.

A general single species ecosystem incorporating Allee effect is proposed and studied in this paper.We show that if the system without Allee effect has unique globally stable positive equilibrium,then the system with Allee effect also admits a unique global stable positive equilibrium.That is,Allee effect has no influence on the position and stability property of the system.However,numeric simulations show that with the increasing of the Allee effect,the system takes much longer time to reach its stable-state solution.