Analysis on existence of bifurcation solutions for a predator-prey model with herd behavior

被引：24
|
作者：
Yang, Wenbin [1 ]
机构：
[1] Xian Univ Posts & Telecommun, Sch Sci, Xian 710121, Shaanxi, Peoples R China
来源：
APPLIED MATHEMATICAL MODELLING | 2018年 / 53卷
关键词：
Predator-prey model; Herd behavior; Reaction-diffusion equations; Bifurcation; QUALITATIVE-ANALYSIS; SYSTEM; DYNAMICS; PATTERNS; STABILITY; HOPF; CHAOS;
D O I：
10.1016/j.apm.2017.09.020
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This paper is concerned with a diffusive predator-prey model with herd behavior. The local and global stability of the unique homogeneous positive steady state U* is obtained. Treating the conversion or consumption rate gamma as the bifurcation parameter, the steady-state bifurcations both from simple and double eigenvalues are studied near U*. The techniques include the Lyapunov function, the spectrum analysis of operators, the bifurcation theory, space decompositions and the implicit function theorem. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：433 / 446
页数：14
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