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

Abstract

Fires and rainfall are major mechanisms that regulate woody and grassy biomasses in savanna ecosystems. Conditions of long-lasting coexistence of trees and grasses have been mainly studied using continuous-time modelling of tree-grass competition. In these frameworks, fire is a time-continuous forcing while the relationship between woody plant size and fire-sensitivity is not systematically considered. In this paper, we propose a new mathematical framework to model tree-grass interaction that takes into account both the discrete nature of fire occurrence and size-dependent fire sensitivity (via two classes of woody plants). We carry out a qualitative analysis that highlights ecological thresholds and bifurcations parameters that shape the dynamics of the savanna-like systems within the main ecological zones. Moreover, through a qualitative analysis, we show that the impulsive modelling of fire occurrences leads to more diverse behaviors and a more realistic array of solutions than the analogous time-continuous fire models. Numerical simulations are provided to illustrate the theoretical results and to support a discussion about the bifurcation parameters and future developments.

42 pages, 5 figures

References in corpus (1)

• Strong interaction between plants induces circular barren patches: fairy circles

Cited by in corpus (4)

• A model for random fire induced tree-grass coexistence in savannas
• Analysis of propagation for impulsive reaction-diffusion models
• Spreading speeds and traveling waves for monotone systems of impulsive reaction-diffusion equations: application to tree-grass interactions in fire-prone savannas
• On the usefulness of a minimalistic model to study tree-grass biomass distributions along biogeographic gradients in the savanna biome