  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.
