A minimalistic model of tree–grass interactions using impulsive differential equations and non-linear feedback functions of grass biomass onto fire-induced tree mortality

Autor: Jean Jules Tewa, Samuel Bowong, Pierre Couteron, Yves Dumont, A. Tchuinté Tamen
Přispěvatelé: University of Yaoundé [Cameroun], Botanique et Modélisation de l'Architecture des Plantes et des Végétations (UMR AMAP), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut National de la Recherche Agronomique (INRA)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Laboratoire International de Recherche en Informatique et Mathématiques Appliquées (LIRIMA), Université de Yaoundé I-Université Badji Mokhtar Annaba (UBMA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Joseph Ki-Zerbo [Ouagadougou] (UJZK)-Université d'Antananarivo-Université Gaston Bergé Sénégal-Centre National de la Recherche Scientifique et Technologique (CNRST), French government, French Embassy in Yaoundé (Cameroon), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Institut National de la Recherche Agronomique (INRA)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut de Recherche pour le Développement (IRD [France-Sud]), Centre National de la Recherche Scientifique et Technologique (CNRST)-Université Gaston Bergé Sénégal-Université d'Antananarivo-Université Joseph Ki-Zerbo [Ouagadougou] (UJZK)-Université Badji Mokhtar - Annaba [Annaba] (UBMA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Yaoundé I, Université de Yaoundé I [Yaoundé]-Université Badji Mokhtar - Annaba [Annaba] (UBMA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Ouagadougou-Université d'Antananarivo-Université Gaston Bergé Sénégal-Centre National de la Recherche Scientifique et Technologique (CNRST)
Jazyk: angličtina
Rok vydání: 2017
Předmět:
0106 biological sciences
0301 basic medicine
Asymptotic stability
forêt tropicale
[SDV.BID.SPT]Life Sciences [q-bio]/Biodiversity/Systematics
Phylogenetics and taxonomy
01 natural sciences
Grassland
Tree–grass interactions
K01 - Foresterie - Considérations générales
Dynamique des populations
Quantitative Biology::Populations and Evolution
Savane
Mathematics
Numerical Analysis
Biomass (ecology)
geography.geographical_feature_category
Impulsive differential equations
Applied Mathematics
Observable
[SDV.BV.BOT]Life Sciences [q-bio]/Vegetal Biology/Botanics
Tree-grass interactions
Compétition végétale
Tree (data structure)
Modeling and Simulation
Forêt
Écosystème forestier
Bifurcation
Biological system
Modèle mathématique
Écosystème
Incendie spontané
General Computer Science
F40 - Écologie végétale
Differential equation
Herbage
010603 evolutionary biology
Fires
Theoretical Computer Science
03 medical and health sciences
[SDV.EE.ECO]Life Sciences [q-bio]/Ecology
environment/Ecosystems
Exponential stability
Compétition biologique
Simulation
geography
Méthode statistique
15. Life on land
Nonlinear system
Complex dynamics
030104 developmental biology
13. Climate action
Incendie de forêt
[SDE.BE]Environmental Sciences/Biodiversity and Ecology
Zdroj: Mathematics and Computers in Simulation
Mathematics and Computers in Simulation, 2017, 133, pp.265-297. ⟨10.1016/j.matcom.2016.03.008⟩
Mathematics and Computers in Simulation, Elsevier, 2017, 133, pp.265-297. ⟨10.1016/j.matcom.2016.03.008⟩
ISSN: 0378-4754
DOI: 10.1016/j.matcom.2016.03.008⟩
Popis: International audience; Since savannas are important ecosystems around the world, their long term dynamics is an important issue, in particular when perturbations, like fires, occur more or less often. In a previous paper, we developed and studied a tree–grass model that take into account fires as pulse events using impulsive differential equations. In this work, we propose to improve this impulsive model by considering the impact of pulse fire on tree biomass by mean of combination of two nonlinear functions of grass and tree biomasses respectively. By considering two impact functions, our model yields more complex dynamics, allowing for the possibility of various bistabilities and periodic solutions, in either grassland or savanna states in the ecosystem. Our mathematical analysis allows extensive and realistic description of savannas ecosystems, than previous modelling approaches. We also highlight several threshold parameters that summarize all possible dynamics, as well as three main parameters of bifurcations in the tree–grass dynamics : the fire period, the tree–grass facilitation/competition parameter, and the fire intensity. Using an appropriate nonstandard numerical scheme, we provide numerical simulations to discuss some ecologically interesting cases that our model is able to exhibit along a rainfall gradient, observable in Central Africa.
Databáze: OpenAIRE
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