2002 Fiscal Year Final Research Report Summary
On behaviors of solutions in non-linear reaction-diffusion systems
| Project/Area Number |
13640141
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | DOSHISHA UNIVERSITY |
|---|
Principal Investigator |
KAWASAKI Kohkichi Doshisha University, Faculty of Engineering, Professor, 工学部, 教授 (10150799)
|
|---|
| Project Period (FY) |
2001 – 2002
|
| Keywords | reaction-diffusion equation / biological invasion / traveling wave / Allee effect / long distance dispersal |
|---|
| Research Abstract |
In this research, we have the following results of the behaviors of solutions in some non-linear reaction-diffusion systems. (1) We investigate a Lotka-Volterra three-competing-species system with diffusion terms and reveal the range expansion behaviors of populations. The populations of three competing species can invade and expand their ranges. The densities of populations are nearly constant during some time interval. After that, the population densities vary in chaos. We also get an approximate expression for the speed of range expansion. (2) We consider a reaction-diffusion system, which describes a dynamics of the population densities with mobile and stationary states. We result that for the growth function with Alee effects, the speed of range expansion is smaller then that for the logistic growth function and also there is a case where the expansion ceases. We also get some estimated expressions for the speed of range expansion in case of equal transition rate between mobile state and stationary one. (3) We consider the range expansion of a population in periodically fragmented environments, which is described by a partial differential equation. We observe some waves called by "traveling periodic wave in tow-dimension (TPW)" and get an implicit formula for the speed of TPW and some patterns of the front edges of population localized at origin at the beginning.
|
