Tree–grass interaction dynamics and pulsed fires: Mathematical and numerical studies

Tchuinte Tamen Alexis, Dumont Yves, Tewa Jean Jules, Bowong Samuel, Couteron Pierre. 2016. Tree–grass interaction dynamics and pulsed fires: Mathematical and numerical studies. Applied Mathematical Modelling, 40 (11-12) : pp. 6165-6197.

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Abstract : Savannas are dynamical systems where grasses and trees can either dominate or coexist. Fires are known to be central in the functioning of the savanna biome although their characteristics are expected to vary along the rainfall gradients as observed in Sub-Saharan Africa. In this paper, we model the tree–grass dynamics using impulsive differential equations that consider fires as discrete events. This framework allows us to carry out a comprehensive qualitative mathematical analysis that revealed more diverse possible outcomes than the analogous continuous model. We investigated local and global properties of the equilibria and we showed that various states exist for the physiognomy of vegetation. Though several shifts between vegetation states appeared to be determined by fire periodicity, we showed that direct shading of grasses by trees is also an influential process embodied in the model by a competition parameter leading to bifurcations. Relying on a suitable nonstandard simulation scheme, we carried out numerical simulations in reference to three main climatic zones as observable in Central Africa. (Résumé d'auteur)

Mots-clés Agrovoc : Savane, forêt tropicale, Écosystème forestier, Herbage, Compétition végétale, Incendie spontané, Pluviométrie, Précipitation, Dynamique des populations, Modèle de simulation, Méthode statistique

Mots-clés géographiques Agrovoc : Afrique centrale, Afrique au sud du Sahara

Mots-clés libres : Savanna, Tree-grass competition, Fires, Impulsive differential equation, Bifurcation, Nonstandard numerical scheme

Classification Agris : K01 - Forestry - General aspects
F40 - Plant ecology
U10 - Computer science, mathematics and statistics

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

Auteurs et affiliations

  • Tchuinte Tamen Alexis, Université de Yaoundé (CMR)
  • Dumont Yves, CIRAD-BIOS-UMR AMAP (FRA) ORCID: 0000-0003-4817-685X
  • Tewa Jean Jules, Université de Yaoundé (CMR)
  • Bowong Samuel, Université de Yaoundé (CMR)
  • Couteron Pierre, IRD (FRA)

Source : Cirad-Agritrop (

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