Turing-Hopf bifurcations in a predator-prey model with herd behavior, quadratic mortality and prey-taxis

被引：46
|
作者：
Liu, Xia [1 ]
Zhang, Tonghua [2 ]
Meng, Xinzhu [3 ,4 ]
Zhang, Tongqian [3 ,4 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China
[2] Swinburne Univ Technol, Dept Math, Hawthorn, Vic 3122, Australia
[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[4] Shandong Univ Sci & Technol, Shandong Prov & Minist Sci & Technol, State Key Lab Min Disaster Prevent & Control, Qingdao 266590, Peoples R China
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2018年 / 496卷
关键词：
Turing pattern; Turing-Hopf bifurcation; Reaction-diffusion equations; Herd behavior; Diffusion; REACTION-DIFFUSION SYSTEM; SPATIOTEMPORAL DYNAMICS; PATTERN-FORMATION; ADDITIONAL FOOD; FUNCTIONAL-RESPONSES; CROSS-DIFFUSION; STABILITY; IMPACTS;
D O I：
10.1016/j.physa.2018.01.006
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we propose a predator-prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：446 / 460
页数：15
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