Impulsive fire disturbance in a savanna model: Tree-grass coexistence states, multiple stable system states, and resilience

TL;DR

This paper models savanna ecosystems using impulsive differential equations to analyze how fire frequency and intensity influence tree-grass coexistence, stability, and resilience, revealing complex bifurcation structures and tipping points.

Contribution

It introduces an impulsive dynamical system approach to better understand fire disturbance effects on savanna stability and social value resilience, highlighting regimes unseen in continuous models.

Findings

Multiple bistability regimes identified

Rich bifurcation structures due to fire disturbances

Small changes can trigger large social value transitions

Abstract

Savanna ecosystems are shaped by the frequency and intensity of regular fires. We model savannas via an ordinary differential equation (ODE) encoding a one-sided inhibitory Lotka-Volterra interaction between trees and grass. By applying fire as a discrete disturbance, we create an impulsive dynamical system that allows us to identify the impact of variation in fire frequency and intensity. The model exhibits three different bistability regimes: between savanna and grassland; two savanna states; and savanna and woodland. The impulsive model reveals rich bifurcation structures in response to changes in fire intensity and frequency -- structures that are largely invisible to analogous ODE models with continuous fire. In addition, by using the amount of grass as an example of a socially-valued function of the system state, we examine the resilience of the social value to different disturbance regimes. We find that large transitions ("tipping") in the valued quantity can be triggered by small changes in disturbance regime.