Modelling Fires as Pulses in Tree/Grass Interactions: Study of Long-term Impact in Forest-Savanna Dynamical Systems
AbstractIt is usually admitted that fires play an important role in tree-grass interactions in savanna ecosystems. In this talk, we present a model of tree-grass dynamics using impulsive differential equations, considering fires as discrete events . This framework allows us to carry out a comprehensive qualitative mathematical analysis that revealed more possible outcomes than the analogous continuous model .В We investigated local and global properties of the equilibria and show that various states may co-exist. Though fire periodicity may drive the system to different and abrupt shifts between vegetation, we also show that direct shading of grasses by trees, through a facilitation/competition parameter, is an influential process too, leading to bifurcations. Finally, using a suitable numerical approach , we carried out numerical simulations related to three main climatic zones, observable in Central Africa, to illustrate our theoretical results.
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