Dynamical analysis of a competition model in the turbidostat with discrete delay

Advances in Difference Equations

Zhijun Liu¹  Hailing Wang¹  Yong Yao¹  Zuxiong Li² 

[1] Department of Mathematics, Hubei University for Nationalities, Enshi, P.R. China;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China

关键词: turbidostat;    bifurcating periodic solutions;    digestion delay;    stability;    competition;   

DOI  :  10.1186/s13662-016-0955-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the dynamic behaviors of a competition model in the turbidostat with discrete delay are investigated. The stability of the positive equilibrium and the existence of a Hopf bifurcation are discussed by choosing the delay of digestion as a bifurcation parameter. Furthermore, we determine the direction and stability of the bifurcating periodic solutions by the normal form and the center manifold theorem. Moreover, some examples are given to illustrate our main results.

【 授权许可】

CC BY