释放毒素的浮游植物与浮游动物相互作用时滞模型分析

曼合布拜·热合木; 李晓娜

doi:10.13568/j.cnki.651094.2019.03.007

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释放毒素的浮游植物与浮游动物相互作用时滞模型分析

更新时间：2026-01-21

- 释放毒素的浮游植物与浮游动物相互作用时滞模型分析
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 36, Issue 3, Pages: 303-311(2019)
- 作者机构：
  
  1. 新疆大学数学与系统科学学院
  2. 伊犁师范大学数学与统计分院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.2019.03.007
  CLC： O175
- Published：2019
- 稿件说明：
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[1]曼合布拜·热合木,李晓娜.释放毒素的浮游植物与浮游动物相互作用时滞模型分析[J].新疆大学学报(自然科学版),2019,36(03):303-311.
[1]曼合布拜·热合木,李晓娜.释放毒素的浮游植物与浮游动物相互作用时滞模型分析[J].新疆大学学报(自然科学版),2019,36(03):303-311. DOI： 10.13568/j.cnki.651094.2019.03.007.

DOI：10.13568/j.cnki.651094.2019.03.007.

摘要

本文研究了浮游动物捕食延迟对浮游植物-浮游动物相互作用的整体动力学影响.首先

文章给出了系统解的正性与有界性;其次

分析了系统平衡点的存在性及稳定性.进一步

建立了当时滞经过阈值时的Hopf分支

模型中的功能反应函数是Tissietxi型的.本文通过分析方法和数值模拟方法得到了模型的定性行为.

Abstract

The present paper aims to investigate a toxic producing phytoplankton(TPP)-zooplankton(a prey-predator interaction) system with the delay. The delay in the zooplankton predation is considered and its effect on the overall dynamics of phytoplankton-zooplankton interaction is studied. Firstly

the nonnegativity and boundedness of solutions are given. Then the existence and stability of the equilibrium are investigated. Furthermore

the occurrence of local Hopf bifurcation is established as the delay crosses a threshold value. The system is modelled via a Tissiet type functional response

analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.

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references

DUINKER J,WEFER G.Das CO2-problem und die rolle des ozeans[J].Naturwissenschaften,1994,81:237-242.

SAHA T,BANDYOPADHYAY M.Dynamical analysis of toxin producing phytoplankton-zooplankton interactions[J].Nonlinear Analysis:Real World Applications,2009,10(1):314-332.

SMAYDA T.What is a bloom?[J].A commentary.Limnol.Oceonogr,1997,42:1132-1336.

SMAYDA T.Bloom dynamics:physiology,hebaviour,trophic effects[J].Limnol.Oceaongr.1997,42(5):1132-1136.

ANDERSON DM.Toxic algae blooms and red tides:a global perspective.In:Okaichi T,Anderson D M,Nemoto T.Red tide[M].New York:biology,environmental science and toxicology,Elsevier,1989.

HALLEGRAEFF GM.A review of harmful algae blooms and the apparent global increase[J].Phycologia,1993,32:79-99.

IVES J.Possible mechanism underlying copepod drazing responses to levels of toxicity in trd tide dinoflagellatea[J].J Exp Mar Biol Ecol,1987,112:131-145.

MUKHOPADHYAY B,BHATTACHARYYA R.Modelling phytoplankton allelopathy in a nutrient-plankton model with spatial heterogeneity[J].Ecol Model,2006,198(1-2):163-173.

CUSHING J M.Integrodifferential equations and delay models in population dynamics[M].Heidelberg:Springer,1977.

KUANG Y.Delay differential equations with applications in population dynamics[M].New York:Academic Press,1993.

MACDONALD N.Bological delay system:linear stsbility theory[M].Cambridge:Cambridge University Press,1989.

BERETTA E,KUANG Y.Geometric stability switch criteria in delay differential systens with delay dependant parameters[J].SIAM J Math Anal,2002,33:1144-1165.

CHENG Y F,Mehbuba Rehim.Study of a phytoplankton-zooplankton Interaction model with Delay[J],J Xinjiang Univ(Natural Sci Ed),2013,30(3),297-303.

ZHANG Z Z,Mehbuba Rehim.Global stability in a zooplankton-phytoplankton model[J],J Xinjiang Univ(Natural Sci Ed),2015,32(4),410-417.

GAZI N H,BANDYOPADHYAY M.Effect of time delay on a harvested predator-prey model[J].J Appl Math Comput,2008,26:263-280.

CHATTOPADHYAY J,SARKAR R R,ABDLLAOUI A.A delay differential equation model on harmful algal blooms in the presence of toxic substances[J].IMA J Math Appl Med Biol,2002,19:137-161.

Fu G,Ma W,RUAN S.Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake[J].Chaos Solutions Fractals,2005,23(3):873-886.

HALE J,LUNEL S V.Introduction to functional differential equation[M].New York:Springer,1993.

SAHA T,BANDYOPADHYAY M.Dynamical analysis of toxin producing phytoplankton-zooplankton interactions[J].Nonlinear Anal Real Word APPL,2009,10:314-332.

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