多重时滞富营养化生态模型的稳定性与分支分析  

STABILITY AND BIFURCATION ANALYSIS OF MULTIPLE TIME DELAY EUTROPHICATION ECOLOGICAL MODEL

作　　者：杨纪华[1,2] 刘媚[1] YANG Ji-hua LIU Mei(School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China School of Mathematical Science, Beijing Normal University, Beijing 100875, China)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000 [2]北京师范大学数学科学学院,北京100875

出　　处：《数学杂志》2016年第6期1222-1230,共9页Journal of Mathematics

基　　金：国家自然科学基金资助(11361046);宁夏自然科学基金(NZ13213);宁夏高等学校科研项目(宁教高[2014]222号(17);宁教高[2014]222号(16))

摘　　要：本文研究了多重时滞富营养化生态模型的稳定性与分支问题.利用特征值方法,分别研究了具有单时滞和双时滞模型的线性稳定性.发现当模型中的时滞经过一系列临界值时,模型在平衡点附近经历了Hopf分支和Hopf-zero分支,并给出Hopf分支和Hopf-zero分支存在的充分条件.最后数值模拟验证了理论结果.In this paper,the stability and bifurcation problem of eutrophication ecological model with two time delays is studied.By using the eigenvalue method,we study the linear stabilities with one delay and two delays,respectively.It is found that Hopf bifurcations and Hopf-zero bifurcations exist at the equilibriums when the delays pass through a sequence of critical values.The sufficient conditions of the existence of Hopf bifurcation and Hopf-zero Bifurcation are obtained.In the end,some numerical simulations are carried out for supporting the analytic results.

关 键 词：双时滞 稳定性 HOPF分支 Hopf-zero分支 

分 类 号：O175[理学—数学]