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

被引：0
作者：
Xiaosong Tang
Yongli Song
Tonghua Zhang
机构：
[1] Tongji University,Department of Mathematics
[2] Jinggangshan University,College of Mathematics and Physics
[3] Swinburne University of Technology,Department of Mathematics
来源：
Nonlinear Dynamics | 2016年 / 86卷
关键词：
Predator–prey model; Herd behavior; Cross-diffusion; Turing–Hopf bifurcation; Spatially inhomogeneous periodic solution;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：73 / 89
页数：16
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