Short note on a solution with large amplitude for the limiting system arising from the competition-diffusion system

Abstract

Abstract This paper is concerned with positive solutions of the limiting system arising from the Shigesada–Kawasaki–Teramoto model with large interspecific competition rate. It has previously been suggested that the limiting system has positive solutions with large amplitude for a certain value of parameters. As a first step, the purpose of this paper is to discuss the precise spatial profile of such solutions by employing formal calculations by the singular perturbation technique.

Keywords

• Competition-diffusion system
• Limiting system
• Positive solution with large amplitude
• Spatial profile