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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number1550117
JournalInternational Journal of Bifurcation and Chaos
Volume25
Issue number9
DOIs
Publication statusPublished - 2015 Aug 8

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

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