Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth

Advances in Difference Equations

Yongfeng Wu¹  Ling Hu²  Huiping Fang² 

[1] School of Mathematics and Finance, Chuzhou University;School of Mathematics and Statistics, Huangshan University;

关键词: Diffusion;    Delay;    Simth growth;    Positive equilibrium;    Hopf bifurcation;   

DOI  :  10.1186/s13662-018-1726-4

来源: DOAJ

【 摘 要 】

Abstract In this paper, we study a diffusion Holling–Tanner predator–prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration technique and eigenvalue analysis to get the local stability and a Hopf bifurcation at the positive equilibrium. Secondly, by choosing the constant related to delay as bifurcation parameter we obtain periodic solutions near the positive equilibrium. Besides, by using center manifold theory and normal form theory we reflect the stability with Hopf bifurcating periodic solution and bifurcating direction.

【 授权许可】

Unknown