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

Yatat V., Dumont Y., Tewa J.J., Couteron P., Bowong S.. 2014. Biomath, 3 (1) : 18 p..

DOI: 10.11145/j.biomath.2014.04.212

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 : modèle mathématique; compétition végétale; incendie; facteur climatique; plante herbacée; arbre; savane; cameroun

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