The joint effects of diffusion and delay on the stability of a ratio-dependent predator-prey model

Advances in Difference Equations

Kejun Zhuang¹  Gao Jia² 

[1] Business School, University of Shanghai for Science and Technology, Shanghai, China;School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, China

关键词: predator-prey system;    Hopf bifurcation;    reaction-diffusion system;    delay;    35K57;    35B32;    92D25;   

DOI  :  10.1186/s13662-017-1096-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper is concerned with a diffusive and delayed predator-prey system with Leslie-Gower and ratio-dependent Holling type III schemes subject to homogeneous Neumann boundary conditions. Preliminary analyses on the well-posedness of solutions and the dissipativeness of the system are presented with assistance of inequality technique. Then the Hopf bifurcation induced by spatial diffusion and time delay is discussed, respectively. Moreover, the bifurcation properties are obtained by computing the norm forms on the center manifold. Finally, some numerical simulations and conclusions are given to verify and illustrate the theoretical results.

【 授权许可】

CC BY