Open AccessInvasive speed for a competition-diffusion system with three species
Author(s) -
Chaohong Pan,
Hongyong Wang,
Chunhua Ou
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021194
Subject(s) - competition (biology) , diffusion , speedup , nonlinear system , competition model , computer science , focus (optics) , determinacy , mathematics , control theory (sociology) , algorithm , physics , mathematical analysis , ecology , artificial intelligence , economics , biology , optics , parallel computing , market economy , control (management) , quantum mechanics , thermodynamics , welfare
Competition stems from the fact that resources are limited. When multiple competitive species are involved with spatial diffusion, the dynamics becomes even complex and challenging. In this paper, we investigate the invasive speed to a diffusive three species competition system of Lotka-Volterra type. We first show that multiple species share a common spreading speed when initial data are compactly supported. By transforming the competitive system into a cooperative system, the determinacy of the invasive speed is studied by the upper-lower solution method. In our work, for linearly predicting the invasive speed, we concentrate on finding upper solutions only, and don't care about the existence of lower solutions. Similarly, for nonlinear selection of the spreading speed, we focus only on the construction of lower solutions with fast decay rate. This greatly develops and simplifies the ideas of past references in this topic.