ncku-talk2024-04-25

Colloquium

DATE 2024-04-25　15:10-16:00

PLACE 數學系館 1F3174教室

SPEAKER Toshiyuki Ogawa 教授（日本明治大學）

TITLE Traveling Wave Solutions in Three-Component Competition-Diffusion Systems

ABSTRACT Segregation is one of the important issues in ecology. Several simple situations have been proposed that enable segregation by using mathematical model approach. In particular, the Lotka-Volterra type competition reaction-diffusion model is often studied, and here we are going to focus on the case that we have three competing species. Moreover, we consider the situation where an exotic species invades to the buffer zone between the native two strong species. Since we already know the existence and stability of traveling wave solution connecting two stable constant states in 2-componet strong competition reaction diffusion system, we consider 3-component extended competition system. The original 2-component traveling wave with no third species is again a trivial solution for the 3-component system as well. We focus on the stability change of this trivial traveling wave solution with respect to the intrinsic growth rate for the third species and study the bifurcation structure around it. We are also going to discuss further global bifurcation structure relating to this problem.
This talk is based on the joint works between Chiun-Chuan Chen, Chueh-Hsin Chang, Shin-ichiro Ei, Hideo Ikeda, and Masayasu Mimura.

Colloquium

DATE	2024-04-25　15:10-16:00

PLACE	數學系館 1F3174教室

SPEAKER	Toshiyuki Ogawa 教授（日本明治大學）

TITLE	Traveling Wave Solutions in Three-Component Competition-Diffusion Systems

ABSTRACT	Segregation is one of the important issues in ecology. Several simple situations have been proposed that enable segregation by using mathematical model approach. In particular, the Lotka-Volterra type competition reaction-diffusion model is often studied, and here we are going to focus on the case that we have three competing species. Moreover, we consider the situation where an exotic species invades to the buffer zone between the native two strong species. Since we already know the existence and stability of traveling wave solution connecting two stable constant states in 2-componet strong competition reaction diffusion system, we consider 3-component extended competition system. The original 2-component traveling wave with no third species is again a trivial solution for the 3-component system as well. We focus on the stability change of this trivial traveling wave solution with respect to the intrinsic growth rate for the third species and study the bifurcation structure around it. We are also going to discuss further global bifurcation structure relating to this problem. This talk is based on the joint works between Chiun-Chuan Chen, Chueh-Hsin Chang, Shin-ichiro Ei, Hideo Ikeda, and Masayasu Mimura.