带有再生养分流的海洋生物群落的生长模型及其渐近性态

THE MODEL AND ITS LIMITING BEHAVOUR FOR COMPETING SPECIES IN OCEANS WITH DELAYED NUTRIENT RECYCLING

本文建立了具有一般养分吸收功能的多种海洋生物种群的生长模型,各种群为了争夺共同的资源而竞争,外界资源供给增量是时间的有界函数,一般地带有滞后的再生养分流补充,并且考虑各种群间竞争因素和每个种群内部的干扰因素。该文讨论了模型的有界性,并证明了当干扰常数m<1时,所考虑的生物群落是永久持续生存的,即每个种群都有正的上下限,当m=1时,在再生养分无滞后时建立了若干种群灭绝的充分条件和持续生存的必要条件。

In this poper, we consider the model of the oceanic biological system with a general nutrientuptake function and delayed nutrient recycling. The species compete each other for a single essentialnutrient. Under the assumption that input of the nutrient variations is bounded, and there exist the mu-tual interference of each species and the competition of n species. We discuss the boundness of the solu-tion and prove that when the interference constant m<1, the persistence of all species is establishedand doesnot depend on the harvest. When m=1 and the time lag in the recycling term may be neglect-ed, We obtain some sufficient condition for the extinction of the species and necessary condition forthe persistence of the species.