一类考虑外来有机物的湖泊生态系统的数学模型及稳定性分析  

Dynamical Analysis on a Class of Cross Ecosystem Resources-Phytoplankton-Zooplankton Model

作　　者：黄志伟[1] 贺国峰 黄刚[1] HUANG Zhiwei;HE Guofeng;HUANG Gang(School of Mathematic and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中国地质大学

出　　处：《应用数学》2020年第1期36-44,共9页Mathematica Applicata

基　　金：国家自然科学基金(11571326)

摘　　要：本文提出并研究外来有机物-浮游植物-浮游动物数学模型.首先构造合适的Lyapunov函数然后利用LaSalle不变性原理,证明动力系统的全局稳定性.基于理论分析,发现外来有机物对湖泊生态系统的稳定性有很大影响.特别的,如果单位时间内外来有机物的流入量足够大则会导致浮游植物的灭绝.同时,一些关于控制水华现象的建议被提出.并且模型稳定性分析的结果很好地符合与外来有机物相关的几个假设.In this paper,cross ecosystem resources-phytoplankton-zooplankton model is proposed and studied.By constructing Lyapunov function and using the LaSalle invariance principle,the global stability of the equilibrial is obtained.Based on the theoretical results of the model,we find that the cross ecosystem resources have a large impact on the stability of the marine ecosystem.Furthermore,it may cause the extinction of the phytoplankton.Some suggestions on controlling the phytoplankton blooms are proposed.In particular,the results of our model fit well with three hypothesises related to the cross ecosystem resources.

关 键 词：湖泊生态系统 数学模型 稳定性分析 水华现象 

分 类 号：O175.13[理学—数学]