@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},
}