Effects of boundary conditions on pattern formation in a nonlocal prey-predator model

被引：16

作者：

Pal, Swadesh ^{[1
]}

Banerjee, Malay ^{[1
]}

Ghorai, S. ^{[1
]}

机构：

[1] IIT Kanpur, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

来源：

APPLIED MATHEMATICAL MODELLING | 2020年 / 79卷 / 809-823期

关键词：

Nonlocal model; Kernel function; Turing bifurcation; Spatial-Hopf bifurcation; Neumann boundary condition; Periodic boundary condition; STOCHASTIC MODEL; GLOBAL STABILITY; LESLIE-GOWER; SYSTEMS; WAVES;

D O I：

10.1016/j.apm.2019.10.061

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Effects of periodic and Neumann boundary conditions on a nonlocal prey-predator model are investigated. Two types of kernel functions with finite supports are used to characterize the nonlocal interactions. These kernel functions are modified to handle the Neumann boundary condition. Numerical techniques to find the Turing and spatial-Hopf thresholds for Neumann boundary condition are also described. For a fixed range of nonlocal interaction with a given kernel function, Turing bifurcation curves corresponding to both the boundary conditions are close to each other. The same is true for the spatial-Hopf bifurcation curves too. However, the nonlinear solutions inside the Turing domain as well as spatial-Hopf domain depend on the boundary condition. Thus, boundary conditions play important roles in a nonlocal model of prey-predator interaction. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：809 / 823

页数：15

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