[1]何 舜,李 梅.一类时滞互惠模型的稳定性及Hopf分支研究[J].南京师范大学学报(自然科学版),2019,42(02):65-72.[doi:10.3969/j.issn.1001-4616.2019.02.011]
　He Shun,Li Mei.Stability and Hopf Bifurcation Analysis in a Mutualistic Model with Time-Delay[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(02):65-72.[doi:10.3969/j.issn.1001-4616.2019.02.011]
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一类时滞互惠模型的稳定性及Hopf分支研究()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第42卷
期数:
2019年02期
页码:
65-72
栏目:
·数学与计算机科学·
出版日期:
2019-06-30

文章信息/Info

Title:
Stability and Hopf Bifurcation Analysis in a Mutualistic Model with Time-Delay
文章编号:
1001-4616(2019)02-0065-08
作者:
何 舜; 李 梅
南京财经大学应用数学学院,江苏 南京 210023
Author(s):
He Shun; Li Mei
School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,China
关键词:
时滞; 互惠模型; 全局稳定性; Hopf分支
Keywords:
time-delay; mutualistic model; global stability; Hopf bifurcation
分类号:
O175.1
DOI:
10.3969/j.issn.1001-4616.2019.02.011
文献标志码:
A
摘要:
本文研究一类带有时滞的互惠种群模型. 首先利用比较定理证明了在ε1ε2≠0时解的有界性,通过构造Lyapunov函数,给出了正平衡解具有全局稳定性的充分条件. 利用特征值理论且以时滞为参数,研究系统hopf分支的存在性,并给出了分支值存在的充分条件. 最后用Matlab绘制出模型数值解的图像,验证所得结论的正确性.
Abstract:
This paper considers a mutualistic model with time-delay. The boundedness of solution is proved by comparison principle when ε1ε2≠0,and sufficient conditions for the global asymptotical stability of the positive equilibrium of the model are obtained by constructing Lyapunov function. Then by using the eigenvalue theory and taking the time delay as the parameter,the existence of Hopf branch of the system is studied,and the sufficient conditions for the existence of branch value are given. Finally,numerical simulations are given to verify the correctness of the theory.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-11-19.
通讯联系人:李梅,博士,教授,研究方向:偏微分方程、随机微分方程. E-mail:9120021078@nufe.edu.cn
更新日期/Last Update: 2019-06-30