Mathematical analysis of a size structured tree-grass competition model for savanna ecosystems

Yatat Valaire, Dumont Yves, Tewa Jean Jules, Couteron Pierre, Bowong Samuel. 2014. Mathematical analysis of a size structured tree-grass competition model for savanna ecosystems. Biomath, 3 (1), 18 p.

https://doi.org/10.11145/j.biomath.2014.04.212

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Résumé : Several continuous-time tree-grass competition models have been developed to study conditions of long-lasting coexistence of trees and grass in savanna ecosystems according to environmental parameters such as climate or fire regime. In those models, fire intensity is a fixed parameter while the relationship between woody plant size and fire-sensitivity is not systematically considered. In this paper, we propose a mathematical model for the tree-grass interaction that takes into account both fire intensity and size-dependent sensitivity. The fire intensity is modeled by an increasing function of grass biomass and fire return time is a function of climate. We carry out a qualitative analysis that highlights ecological thresholds that summarize the dynamics of the system. Finally, we develop a non-standard numerical scheme and present some simulations to illustrate our analytical results.

Mots-clés Agrovoc : modèle mathématique, compétition végétale, incendie, facteur climatique, plante herbacée, arbre, savane

Mots-clés géographiques Agrovoc : Cameroun

Classification Agris : U10 - Informatique, mathématiques et statistiques
F40 - Écologie végétale

Champ stratégique Cirad : Axe 6 (2014-2018) - Sociétés, natures et territoires

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