scholarly journals On the bifurcation structure of positive stationary solutions for a competition-diffusion system

2019 ◽  
Author(s):  
Yukio Kan-on
Keyword(s):  
Stationary Solutions ◽  
Diffusion System ◽  
Bifurcation Structure ◽  
Competition Diffusion

On the Structure of Positive Solutions for the Shigesada–Kawasaki–Teramoto Model with Large Interspecific Competition Rate

2020 ◽  
Vol 30 (01) ◽  
pp. 2050001
Author(s):  
Yukio Kan-on
Keyword(s):  
Positive Solution ◽  
Interspecific Competition ◽  
Positive Solutions ◽  
Comparison Principle ◽  
Nonlinear Diffusion ◽  
Bifurcation Theory ◽  
Diffusion System ◽  
Bifurcation Structure ◽  
Diffusion Term ◽  
Competition Diffusion

In this paper, we treat the competition-diffusion system with nonlinear diffusion term, which was proposed by Shigesada et al. [1979], and discuss the bifurcation structure of positive solution for the system when the interspecific competition rate is sufficiently large. To do this, we derive two kinds of limiting systems as the interspecific competition rate tends to infinity, and study the bifurcation structure of positive solution for each limiting system by employing the comparison principle and the bifurcation theory.

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