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Fires and rainfall are major mechanisms that regulate woody and grassybiomasses in savanna ecosystems. Conditions of long-lasting coexistence oftrees and grasses have been mainly studied using continuous-time modelling oftree-grass competition. In these frameworks, fire is a time-continuous forcingwhile the relationship between woody plant size and fire-sensitivity is notsystematically considered. In this paper, we propose a new mathematicalframework to model tree-grass interaction that takes into account both thediscrete nature of fire occurrence and size-dependent fire sensitivity (via twoclasses of woody plants). We carry out a qualitative analysis that highlightsecological thresholds and bifurcations parameters that shape the dynamics ofthe savanna-like systems within the main ecological zones. Moreover, through aqualitative analysis, we show that the impulsive modelling of fire occurrencesleads to more diverse behaviors and a more realistic array of solutions thanthe analogous time-continuous fire models. Numerical simulations are providedto illustrate the theoretical results and to support a discussion about thebifurcation parameters and future developments.

An impulsive modelling framework of fire occurrence in a size structured model of tree-grass interactions for savanna ecosystems