Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting

Advances in Difference Equations

article

Yu, Xiangqin¹  Zhu, Zhenliang¹  Lai, Liyun¹  Chen, Fengde¹ 

[1] College of Mathematics and Computer Science, Fuzhou University

关键词: Stage structure;    Michaelis–Menten-type harvesting;    Stability;    Bifurcation;   

DOI  :  10.1186/s13662-020-02652-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we prpose a single-species stage structure model with Michaelis–Menten-type harvesting for mature population. We investigate the existence of all possible equilibria of the system and discuss the stability of equilibria. We use Sotomayor’s theorem to derive the conditions for the existence of saddle-node and transcritical bifurcations. From the ecological point of view, we analyze the effect of harvesting on the model of mature population and consider it as a bifurcation parameter, giving the maximum threshold of continuous harvesting. By constructing a Lyapunov function and Bendixson–Dulac discriminant, we give sufficient conditions for the global stability of boundary equilibrium and positive equilibrium, respectively. Our study shows that nonlinear harvesting may lead to a complex dynamic behavior of the system, which is quite different from linear harvesting. We carry out numeric simulations to verify the feasibility of the main results.

【 授权许可】

CC BY