Traveling waves for the reaction-diffusion systems describing the dynamics of invasion processes

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540156
• 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: Kyoto Sangyo University
• Principal Investigator: HOSONO Yuzo 京都産業大学, 理学部, 教授 (50008877)
• Co-Investigator(Kenkyū-buntansha): TSUJII Yoshiki 京都産業大学, 理学部, 教授 (90065871)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 反応拡散系 / 進行波解 / 侵入過程 / 餌食と捕食者モデル / ２種競争系モデル / 侵入速度 / 相空間解析 / 特異摂動法

Outline of Final Research Achievements

The major result of this research consists of the following two parts. (1) We investigate the traveling waves describing the process that the predator invades the region already occupied by the prey, and prove the existence of such traveling waves with any positive speed for a diffusive Lotka-Volterra predator-prey model with no predator diffusion. Our mathematical tool is the shooting argument in the phase space. (2) We also discuss the effect of interspecific competition on the dynamics of neutral genetic diversity in a range-expanding population using a traveling wave solution for a diffusive Lotka-Volterra competition model. Our analytical and numerical results show that the genetic diversity in the invasive population is affected by the interspecific competition rate. Furthermore, we show numerically that the analytical results on the speeds of traveling waves obtained previously, can still be improved.

Free Research Field

数物系科学