@article{fdi:010048367,
title = {{S}tudy of a virus-bacteria interaction model in a chemostat : application of geometrical singular perturbation theory},
author = {{P}oggiale, {J}. {C}. and {A}uger, {P}ierre and {C}ordoleani, {F}. and {N}guyen-{H}uu, {T}ri},
editor = {},
language = {{ENG}},
abstract = {{T}his paper provides a mathematical analysis of a virus-marine bacteria interaction model. {T}he model is a simplified case of the model published and used by {M}iddelboe ({M}iddelboe, {M}. 2000 {M}icrob. {E}col. 40, 114-124). {I}t takes account of the virus, the susceptible bacteria, the infected bacteria and the substrate in a chemostat. {W}e show that the numerical values of the parameters given by {M}iddelboe allow two different time scales to be considered. {W}e then use the geometrical singular perturbation theory to study the model. {W}e show that there are two invariant submanifolds of dimension two in the four-dimensional phase space and that these manifolds cross themselves on the boundary of the domain of biological relevance. {W}e then perform a rescaling to understand the dynamics in the vicinity of the intersection of the manifolds. {O}ur results are discussed in the marine ecological context.},
keywords = {invariant manifold ; reduction ; singular perturbation ; virus-bacteria interaction},
booktitle = {},
journal = {{P}hilosophical {T}ransactions of the {R}oyal {S}ociety a - {M}athematical {P}hysical and {E}ngineering {S}ciences},
volume = {367},
numero = {1908},
pages = {4685--4697},
ISSN = {1364-503{X}},
year = {2009},
DOI = {10.1098/rsta.2009.0132},
URL = {https://www.documentation.ird.fr/hor/fdi:010048367},
}