Time-delay effect on a diffusive predator–prey model with habitat complexity

Advances in Difference Equations

Haicheng Liu¹  Yanfeng Li²  Ruizhi Yang³ 

[1] College of Mathematical Sciences, Harbin Engineering University, 150001, Harbin, Heilongjiang, P.R. China;College of Science, Heilongjiang Bayi Agricultural University, 163319, Daqing, Heilongjiang, P.R. China;Department of Mathematics, Northeast Forestry University, 150040, Harbin, Heilongjiang, P.R. China;

关键词: Predator–prey;    Habitat complexity;    Time delay;    Diffusion term;    Hopf bifurcation;    34K18;    35B32;   

DOI  :  10.1186/s13662-021-03473-y

来源: Springer

【 摘 要 】

Based on the predator–prey system with a Holling type functional response function, a diffusive predator–prey system with digest delay and habitat complexity is proposed. Firstly, the stability of the equilibrium of diffusion system without delay is studied. Secondly, under the Neumann boundary conditions, taking time delay as the bifurcation parameter, by analyzing the eigenvalues of linearized operator of the system and using the normal form theory and center manifold method of partial functional differential equations, the effect of time delay on the stability of the system is studied and the conditions under which Hopf bifurcation occurs are given. In addition, the calculation formulas of the bifurcation direction and the stability of bifurcating periodic solutions are derived. Finally, the accuracy of theoretical analysis results is verified by numerical simulations and the biological explanation is given for the analysis results.

【 授权许可】

CC BY