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

Ana Yun; Jaemin Shin; Yibao Li; Seunggyu Lee; Junseok Kim

doi:10.1142/S0218127415501175

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

Ana Yun, Jaemin Shin, Yibao Li, Seunggyu Lee, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Article number	1550117
Journal	International Journal of Bifurcation and Chaos
Volume	25
Issue number	9
DOIs	https://doi.org/10.1142/S0218127415501175
Publication status	Published - 2015 Aug 8

Bibliographical note

Funding Information:
The first author (A. Yun) acknowledges the support of the National Junior research fellowship from the National Research Foundation of Korea grant funded by the Korea government (No. 2011-00012258). The author (J. Shin) is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The corresponding author (J. S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.

Publisher Copyright:
© 2015 World Scientific Publishing Company.

Keywords

Dirichlet boundary
landscape features
numerical periodicity
periodic traveling waves
predator-prey model

ASJC Scopus subject areas

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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

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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author = "Ana Yun and Jaemin Shin and Yibao Li and Seunggyu Lee and Junseok Kim",

note = "Funding Information: The first author (A. Yun) acknowledges the support of the National Junior research fellowship from the National Research Foundation of Korea grant funded by the Korea government (No. 2011-00012258). The author (J. Shin) is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The corresponding author (J. S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper. Publisher Copyright: {\textcopyright} 2015 World Scientific Publishing Company.",

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N1 - Funding Information: The first author (A. Yun) acknowledges the support of the National Junior research fellowship from the National Research Foundation of Korea grant funded by the Korea government (No. 2011-00012258). The author (J. Shin) is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The corresponding author (J. S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper. Publisher Copyright: © 2015 World Scientific Publishing Company.

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Y1 - 2015/8/8

N2 - 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.

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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