Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains

Sangkwon Kim, Jintae Park, Chaeyoung Lee, Darae Jeong, Yongho Choi, Soobin Kwak and Junseok Kim

Chaos, Solitons & Fractals, 2020, vol. 139, issue C

Abstract: 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.

Keywords: Distance function; Periodic travelling waves; Reaction-diffusion system; Landscape features (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306962

DOI: 10.1016/j.chaos.2020.110300

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