TY - JOUR
T1 - Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains
AU - Kim, Sangkwon
AU - Park, Jintae
AU - Lee, Chaeyoung
AU - Jeong, Darae
AU - Choi, Yongho
AU - Kwak, Soobin
AU - Kim, Junseok
N1 - Funding Information:
The corresponding author (J. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/10
Y1 - 2020/10
N2 - In this article, we propose a new landscape fitted domain construction and its boundary treatment of periodic travelling wave solutions for a diffusive predator-prey system with landscape features. The proposed method uses the distance function based on an obstacle. The landscape fitted domain is defined as a region whose distance from the obstacle is positive and less than a pre-defined distance. At the exterior boundary of the domain, we use the zero-Neumann boundary condition and define the boundary value from the bilinearly interpolated value in the normal direction of the distance function. At the interior boundary, we use the homogeneous Dirichlet boundary condition. Typically, reaction-diffusion systems are numerically solved on rectangular domains. However, in the case of periodic travelling wave solutions, the boundary treatment is critical because it may result in unexpected chaotic pattern. To avoid this unwanted chaotic behavior, we need to use sufficiently large computational domain to minimize the boundary treatment effect. Using the proposed method, we can get accurate results even though we use relatively small domain sizes.
AB - In this article, we propose a new landscape fitted domain construction and its boundary treatment of periodic travelling wave solutions for a diffusive predator-prey system with landscape features. The proposed method uses the distance function based on an obstacle. The landscape fitted domain is defined as a region whose distance from the obstacle is positive and less than a pre-defined distance. At the exterior boundary of the domain, we use the zero-Neumann boundary condition and define the boundary value from the bilinearly interpolated value in the normal direction of the distance function. At the interior boundary, we use the homogeneous Dirichlet boundary condition. Typically, reaction-diffusion systems are numerically solved on rectangular domains. However, in the case of periodic travelling wave solutions, the boundary treatment is critical because it may result in unexpected chaotic pattern. To avoid this unwanted chaotic behavior, we need to use sufficiently large computational domain to minimize the boundary treatment effect. Using the proposed method, we can get accurate results even though we use relatively small domain sizes.
KW - Distance function
KW - Landscape features
KW - Periodic travelling waves
KW - Reaction-diffusion system
UR - http://www.scopus.com/inward/record.url?scp=85091343357&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2020.110300
DO - 10.1016/j.chaos.2020.110300
M3 - Article
AN - SCOPUS:85091343357
SN - 0960-0779
VL - 139
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 110300
ER -