@article{fdi:010069518,
  title = {{A}n impulsive modelling framework of fire occurrence in a size-structured model of tree-grass interactions for savanna ecosystems},
  author = {{Y}atat, {V}. and {C}outeron, {P}ierre and {T}ewa, {J}. {J}. and {B}owong, {S}. and {D}umont, {Y}.},
  editor = {},
  language = {{ENG}},
  abstract = {{F}ires and mean annual rainfall are major factors that regulate woody and grassy biomasses in savanna ecosystems. {W}ithin the savanna biome, conditions of long-lasting coexistence of trees and grasses have been often studied using continuous-time modelling of tree-grass competition. {I}n these studies, fire is a time-continuous forcing while the relationship between woody plant size and fire-sensitivity is not systematically considered. {I}n this paper, we propose a new mathematical framework to model tree-grass interactions that takes into account both the impulsive nature of fire occurrence and size-dependent fire sensitivity (via two classes of woody plants). {W}e carry out a qualitative analysis that highlights ecological thresholds and bifurcation parameters that shape the dynamics of the savanna-like systems within the main ecological zones. {T}hrough a qualitative analysis, we show that the impulsive modelling of fire occurrences leads to more diverse behaviors including cases of grassland, savanna and forest tristability and a more realistic array of solutions than the analogous time-continuous fire models. {N}umerical simulations are carried out with respect to the three main ecological contexts (moist, mesic, semi-arid) to illustrate the theoretical results and to support a discussion about the bifurcation parameters and the advantages of the model.},
  keywords = {{S}avanna ; {F}ire ; {A}symmetric competition ; {I}mpulsive differential equation ; {Q}ualitative analysis ; {N}onstandard finite difference scheme},
  booktitle = {},
  journal = {{J}ournal of {M}athematical {B}iology},
  volume = {74},
  numero = {6},
  pages = {1425--1482},
  ISSN = {0303-6812},
  year = {2017},
  DOI = {10.1007/s00285-016-1060-y},
  URL = {https://www.documentation.ird.fr/hor/fdi:010069518},
}