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

TL;DR

This paper introduces a new impulsive mathematical model for savanna ecosystems that accounts for discrete fire events and size-dependent fire sensitivity of woody plants, providing more realistic dynamics than traditional continuous models.

Contribution

The study develops a novel impulsive modeling framework for tree-grass interactions that incorporates fire discreteness and size-dependent sensitivity, advancing ecological modeling of savannas.

Findings

Impulsive models exhibit more diverse ecological behaviors.

Size-dependent fire sensitivity influences system dynamics.

Bifurcation analysis reveals critical ecological thresholds.

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.