基于水资源竞争的毒杂草入侵扩散模型稳定性分析  

The Stability Analysis of Poisonous Weeds' Invasion Model Based on the Competition of Water Resources

作　　者：石磊[1] 刘华[1] 蒋芮[1] 魏玉梅[2] 

机构地区：[1]西北民族大学数学与计算机科学学院,甘肃兰州730030 [2]西北民族大学实验中心,甘肃兰州730030

出　　处：《湖北民族学院学报（自然科学版）》2016年第4期365-370,共6页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(31260098);国家民委中青年英才计划项目(〔2014〕121号);西北民族大学研究生科研创新项目(Yxm2016124);2013年西北民族大学创新团队资助项目

摘　　要：以干旱地区植物对水资源的竞争环境为背景,考虑根系的分布范围,建立水资源代谢库,进而建立基于水资源竞争的毒杂草与可食牧草种间竞争模型.同时加入入侵扩散作用,建立基于水资源竞争的毒杂草入侵扩散模型,并且运用微分方程稳定性理论对该模型进行稳定性分析.研究表明:在入侵扩散作用下,毒杂草与可食牧草的共存平衡点由一个增加为两个,增加了共存的可能性.This paper takes the competitive environment as the background of plants for water in arid re-gions.Considering the range of root system distribution,we can build the water metabolic warehouse,then build the inter-species competition model of poisonous weeds,and edible grass based on competition of water resources.At the same time,to join the invasion of diffusion,we build the diffusion model of poison-ous weeds′invasion based on water resources competition,and then analyse its stability by using the sta-bility theory of the ordinary differeatial equations. Research shows that under the influence of the invasion and diffusion,the coexistence equilibrium points of the poisonous weeds and the edible grass could be in-creased to two,which increased the possibility of coexistence.

关 键 词：入侵 稳定性 元胞自动机 

分 类 号：O29[理学—应用数学]