Open AccessWeakly coupled traveling waves for a model of growth and competition in a flow reactor
Author(s) -
Wenzhang Huang
Publication year - 2006
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2006.3.79
Subject(s) - traveling wave , population , interval (graph theory) , competition (biology) , diffusion , organism , flow (mathematics) , reaction–diffusion system , mechanics , carrying capacity , position (finance) , space (punctuation) , physics , environmental science , biological system , ecology , mathematics , biology , mathematical analysis , computer science , economics , thermodynamics , demography , paleontology , finance , combinatorics , sociology , operating system
For a reaction-diffusion model of microbial flow reactor with two competing populations, we show the coexistence of weakly coupled traveling wave solutions in the sense that one organism undergoes a population growth while another organism remains in a very low population density in the first half interval of the space line; the population densities then exchange the position in the next half interval. This type of traveling wave can occur only if the input nutrient slightly exceeds the maximum carrying capacity for these two populations. This means, lacking an adequate nutrient, two competing organisms will manage to survive in a more economical way.