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

Tchuinte Tamen A., Dumont Y., Bowong S., Tewa J.J., Couteron P.. 2016. Perpignan : Université de Perpignan, 1 p.. Emerging Trends in Applied Mathematics and Mechanics Conference (ETAMM 2016), 2016-05-30/2016-06-03, Perpignan (France).

Explanations accounting for tree-grass interactions in savanna ecosystems are of- ten based on either facilitation/competition for resources, or differential sensitivity to fires. We propose a tree-grass model which accounts both phenomena (i.e. competition and _res). In the literature, several models used positive feedback between grass biomass (fuel load) and fire intensity, however, they did not incorporate nonlinear response of _re frequency/intensity to tree biomass. Our model explicitly considers the impact of pulse _re on tree biomass by mean of two non-linear impact functions including the response function of woody biomass to fire intensity. By considering two impact functions, our system yields complex dynamics, allowing for various possibilities of bistability and periodic equilibria in the ecosystem. We investigate local and global properties of equilibria. We highlight three parameters of bifurcations: the _re period, the tree-grass competition parameter, and the _re intensity. Using an appropriate nonstandard numerical scheme, we provide numerical simulations to discuss some ecologically interesting cases our model is able to exhibit along a rainfall gradient. In order to represent spatial patterns observed in different environmental regions, a preliminary work that explicitly represent the spatial interactions among trees and grasses is introduced. (Texte intégral)

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