Speaker: Denis Patterson (Durham University)
Title: Spatial models of forest-savanna bistability
Zoom Link: https://illinois.zoom.us/j/81298771146?pwd=WXFvTEt5ZVEwY0NSWkM4M0JzbnFjUT09
Abstract: Empirical studies suggest that for vast tracts of land in the tropics, closed-canopy forests and savanna are alternative stable states, a proposition with far-reaching implications in the context of ongoing climate change. Consequently, numerous mathematical models, both spatially implicit and explicit, have been proposed to capture the mechanistic basis of this bistability and quantify the stability of these ecosystems. We present analysis of a spatially extended version of the so-called Staver-Levin model of forest-savanna dynamics (a system of nonlinear partial integro-differential equations). On a homogeneous domain, we uncover various types of pattern-forming bifurcations in the presence of resource limitation, which we study as a function of the resource constraints and length scales in the problem. On larger (continental) spatial scales, heterogeneity plays a significant role in determining observed vegetative cover. Incorporating domain heterogeneity leads to interesting phenomena such as front-pinning, complex waves, and extensive multi-stability, which we investigate analytically and numerically.