一类真菌-浮游动物-浮游植物模型分析  

Analysis of a fungus-zooplankton-phytoplankton model

作　　者：王红月 赵治涛[1] WANG Hongyue;ZHAO Zhitao(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2023年第3期275-282,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金(11201128);黑龙江省高校大学专项科研基金(2021-KYYWF-0018)。

摘　　要：浮游动物和浮游植物是水生生物群落的基础。真菌作为重要的水生微生物之一,可以影响浮游动物和浮游植物的生存和繁殖。本文主要研究一类真菌-浮游动物-浮游植物模型,其中浮游动物以浮游植物为食,同时可以被真菌所感染。利用常微分方程比较定理,给出了模型解的耗散性。基于线性稳定分析、渐近自治系统理论和分支理论,建立了模型平衡点的存在性和稳定性。通过数值模拟验证所得理论结果,并指出模型可以产生周期振荡。Zooplankton and phytoplankton are the basis of aquatic communities.Fungi,as one of the important aquatic microorganisms,can influence the survival and reproduction of zooplankton and phytoplankton.A fungus-zooplankton-phytoplankton model is explored,in which zooplankton consumes phytoplankton and can be infected by fungi.The dissipativity of the solutions is given by using the comparison theorem of ordinary differential equations.Based on linear stability analysis,asymptotic autonomous system theory and bifurcation theory,the existence and stability of equilibria of the model are established.The theoretical results are verified by numerical simulations,and it is pointed out that the model can generate periodic oscillations.

关 键 词：真菌-浮游动物-浮游植物模型 耗散性 平衡点 分支理论 数值模拟 

分 类 号：O175.21[理学—数学]