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Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

Authors
Yun, AnaShin, JaeminLi, YibaoLee, SeunggyuKim, Junseok
Issue Date
8월-2015
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Keywords
Dirichlet boundary; periodic traveling waves; predator-prey model; landscape features; numerical periodicity
Citation
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v.25, no.9
Indexed
SCIE
SCOPUS
Journal Title
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume
25
Number
9
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/92824
DOI
10.1142/S0218127415501175
ISSN
0218-1274
Abstract
We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.
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