Effect of predator cannibalism and prey growth on the dynamic behavior for a predator-stage structured population model with diffusion

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Jia, Yunfeng¹  Li, Yi²  Wu, Jianhua¹ 

[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710062, Shaanxi, Peoples R China

[2] Calif State Univ Northridge, Dept Math, Northridge, CA 91325 USA

关键词: Predator-prey model;    Stage structure;    Steady states;    Stability;    Fixed point index;    Hopf bifurcation;   

DOI  :  10.1016/j.jmaa.2016.12.036

来源: Elsevier

【 摘 要 】

In this paper, a predator-prey model with predator-stage structured and diffusion is concerned. We deal with the system by endowing it with the homogeneous Neumann boundary conditions. We first give the a priori estimates of positive solutions for the reduced reaction diffusion system. Secondly, we discuss the effects of predator cannibalism and prey growth on the stability of nonnegative constant steady states of the model in detail. Thirdly, we investigate the nonexistence and existence of nonconstant positive solutions. Finally, we discuss the Hopf bifurcation created by diffusion. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free