On behaviors of solutions in nonlinear reactiondiffusion systems
Project/Area Number 
13640141

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear 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

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)

Keywords  reactiondiffusion 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 nonlinear reactiondiffusion systems. (1) We investigate a LotkaVolterra threecompetingspecies 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 reactiondiffusion 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 towdimension (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.

Report
(3 results)
Research Products
(9 results)