Turing-Hopf bifurcation analysis of a predator-prey model with herd behavior and cross-diffusion

被引：75

作者：

Tang, Xiaosong ^{[1
,2
]}

Song, Yongli ^{[1
]}

Zhang, Tonghua ^{[3
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Jinggangshan Univ, Coll Math & Phys, Jian 343009, Jiangxi, Peoples R China

[3] Swinburne Univ Technol, Dept Math, Hawthorn, Vic 3122, Australia

来源：

NONLINEAR DYNAMICS | 2016年 / 86卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Predator-prey model; Herd behavior; Cross-diffusion; Turing-Hopf bifurcation; Spatially inhomogeneous periodic solution; PATTERN-FORMATION; SPATIOTEMPORAL DYNAMICS; SPATIAL-PATTERNS; INSTABILITY; STABILITY; SYSTEM; SPACE;

D O I：

10.1007/s11071-016-2873-3

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, we consider a predator-prey model with herd behavior and cross-diffusion subject to homogeneous Neumann boundary condition. Firstly, the existence and priori bound of a solution for the model without cross-diffusion are shown. Then, by computing and analyzing the normal form on the center manifold associated with the Turing-Hopf bifurcation, we find a wealth of spatiotemporal dynamics near the Turing-Hopf bifurcation point under suitable conditions. Furthermore, some numerical simulations to illustrate the theoretical analysis are carried out.

引用

页码：73 / 89

页数：17

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