Short note on the position of bifurcation points for the limiting system arising from the two competing species model

Abstract

In this paper, we treat the competition-diffusion system with nonlinear diffusion term, which was proposed by Sigesada, Kawasaki and Teramoto in 1979 to model the segregation of interacting species, and discuss the bifurcation structure of nonnegative solution for the limiting system arising from the competition-diffusion system as the interspecific competition rate tends to $ +\infty $. To do this, we employ the comparison principle and the property of the Bessel function, and study the position of bifurcation points, at which a nonconstant solution bifurcates from the constant solution, for the limiting system.