@article{fdi:010055937,
  title = {{A} review on spatial aggregation methods involving several time scales},
  author = {{A}uger, {P}ierre and {P}oggiale, {J}. {C}. and {S}anchez, {E}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}his article is a review of spatial aggregation of variables for time continuous models. {T}wo cases are considered. {T}he first case corresponds to a discrete space, i.e. a set of discrete patches connected by migrations, which are assumed to be fast with respect to local interactions. {T}he mathematical model is a set of coupled ordinary differential equations ({O}.{D}.{E}.). {T}he spatial aggregation allows one to derive a global model governing the time variation of the total numbers of individuals of all patches in the long term. {T}he second case considers a continuous space and is a set of partial differential equations ({P}.{D}.{E}.). {I}n that case, we also assume that diffusion is fast in comparison with local interactions. {T}he spatial aggregation allows us again to obtain an {O}.{D}.{E}. governing the total population density, which is obtained by integration all over the spatial domain, at the slow time scale. {T}hese aggregations of variables are based on time scales separation methods which have been presented largely elsewhere and we recall the main results. {W}e illustrate the methods by examples in population dynamics and prey-predator models.},
  keywords = {{A}ggregation of variables ; {T}wo time scales ; {S}patially structured ; population dynamics ; {R}eaction-diffusion equations},
  booktitle = {},
  journal = {{E}cological {C}omplexity},
  volume = {10},
  numero = {{SI}},
  pages = {12--25},
  ISSN = {1476-945{X}},
  year = {2012},
  DOI = {10.1016/j.ecocom.2011.09.001},
  URL = {https://www.documentation.ird.fr/hor/fdi:010055937},
}