Modelling fire as discrete events in some tree-grass interaction models with explicit soil water resource

Tchuinte Tamen Alexis, Tewa Jean Jules, Couteron Pierre, Bowong Samuel, Dumont Yves. 2013. Modelling fire as discrete events in some tree-grass interaction models with explicit soil water resource. In : Conference book BIOMATH 2013 (International conference on Mathematical Methods and Models in Biosciences ), Sofia, Bulgaria, 16 June to 21 June 2013. R. Anguelov and E. Nikolova. s.l. : s.n., Résumé, 46. International conference on Mathematical Methods and Models in Biosciences, Sofia, Bulgarie, 16 Juin 2013/21 Juin 2013.

Matériel d'accompagnement : 1 poster

Résumé : Savannah is a grassland ecosystem characterized by various trees density. It occurs in areas with annual rainfall from 300 to 1800 mm. If rainfall plays an important role in this savannah ecosystem, big fire events also can disturb the whole dynamics. Several continuous competition-based models have been proposed to explain different tree-grass patterns, taking into account fire events (see for instance [1] and references therein). We first consider a tree-grass model, but instead of considering continuous fire forcings, we consider fire as discrete events and derive an impulse differential system. A qualitative analysis show that a periodic equilibrium can exist as well as local and global equilibria, according to some threshold parameters. Then, we consider an eco-hydrological model recently published [1], that takes into account rainfall through a soil moisture equation. We perform a mathematical analysis and develop a nonstandard numerical scheme, that is able to preserve all qualitative properties of the model. Finally, using appropriate numerical schemes [3], we perform several numerical simulations. We conclude and present further possible developments.

Classification Agris : U10 - Informatique, mathématiques et statistiques
F40 - Écologie végétale
K01 - Foresterie - Considérations générales

Auteurs et affiliations

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

Source : Cirad - Agritrop (https://agritrop.cirad.fr/571750/)

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