Bifurcation analysis of a turbidostat model with distributed delay

被引：6
作者：
Mu, Yu [1 ]
Li, Zuxiong [1 ,2 ]
Xiang, Huili [1 ,2 ]
Wang, Hailing [1 ,2 ]
机构：
[1] Hubei Univ Nationalities, Dept Math, Enshi 445000, Hubei, Peoples R China
[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
来源：
NONLINEAR DYNAMICS | 2017年 / 90卷 / 02期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Distributed delay; Turbidostat; Hopf bifurcation; Periodic solution; Destabilization; GLOBAL ASYMPTOTIC-BEHAVIOR; CHEMOSTAT MODEL; COMPETITION; STABILITY; NUTRIENT; GROWTH; PERSISTENCE; EQUATIONS;
D O I：
10.1007/s11071-017-3728-2
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, dynamic behaviors of a turbidostat model with distributed delay are concerned. Hopf bifurcations arise when the value of bifurcation parameter, the time delay of translation for the nutrient, crosses some critical values. Firstly, the type and stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Moreover, the destabilization of periodic solutions is also discussed. Finally, numerical simulation results are given to support the theoretical conclusions.
引用
收藏
页码：1315 / 1334
页数：20
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