Hopf bifurcation in delayed nutrient-microorganism model with network structure

Journal of Biological Dynamics

卷:16

Ranchao Wu¹  Liping Chen²  Mengxin Chen³  Qianqian Zheng⁴ 

[1] Anhui University;

[2] Hefei University of Technology;

[3] Henan Normal University;

[4] Xuchang University;

关键词: nutrient-microorganism model;    hopf bifurcation;    amplitude equation;    random network;   

DOI  :  10.1080/17513758.2021.2020915

来源: DOAJ

【 摘 要 】

In this paper, we introduce and deal with the delayed nutrient-microorganism model with a random network structure. By employing time delay τ as the main critical value of the Hopf bifurcation, we investigate the direction of the Hopf bifurcation of such a random network nutrient-microorganism model. Noticing that the results of the direction of the Hopf bifurcation in a random network model are rare, we thus try to use the method of multiple time scales (MTS) to derive amplitude equation and determine the direction of the Hopf bifurcation. It is showed that the delayed random network nutrient-microorganism model can exhibit a supercritical or subcritical Hopf bifurcation. Numerical experiments are performed to verify the validity of the theoretical analysis.

【 授权许可】

Unknown