带扩散种群模型的分析

Analysis of Population Model with Diffusion

考虑允许种群自身在其生存空间存在扩散的情况下,建立一个统一的偏微分模型来描述种群之间的三种关系。分别讨论了三类种群模型的动态变化过程。(1)如果捕食者疯狂猎杀被捕食者,则随着时间的推移,被捕食者因为过度被捕杀而灭绝,捕食者也由于食物的灭绝而灭绝。(2)很好地解释了生态学中的竞争排斥原理:若两种群的单个成员消耗的差不多相同,而环境能承受的种群u的最大容量比种群v大,那么种群v终将灭绝。(3)在强合作的情况下,种群数量会随着时间的增加急剧增加以致环境所允许的容量破坏生态系统的平衡,所以弱合作(相互之间的促进不是很强)比强合作更有利于保持生态系统的平衡.

In order to describe three kinds of relationships between the populations,we establish a partial differential model with diffusion and discuss the dynamic process of them.（1）If predators kill the prey crazily,as time goes on,the prey and the predators will die out.（2）It＇s good to illustrate the theory of the competition exclusion in the bionomy：if the individual of the two groups use up the resources nearly and the capacity of environment＇s endurement u is larger than that of v,the group v will die out.（3） In the strong cooperation,the number of the group will increase rapidly as time goes on,which leads to destroying the balance of the bionomic system,so the weak cooperation is better to keep the balance of the bionomic system than the strong one.