  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
though 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 show that various states exist for the physiognomy of
vegetation. Though several abrupt shifts between vegetation states appeared
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 finite
difference scheme, we carried out numerical simulations in reference to three
main climatic zones as observable in Central Africa.
