2018/08/24 by Rick Durrett, Durrett, Rick, Ruibo Ma +1
Medicine · Environmental Science · #Mathematical and Theoretical Epidemiology and Ecology Models #Ecology and Vegetation Dynamics Studies #Ecosystem dynamics and resilience
paper · pdf · doi:10.48550/arxiv.1808.08159
In work with a variety of co-authors, Staver and Levin have argued that savanna and forest coexist as alternative stable states with discontinuous changes in density of trees at the boundary. Here we formulate a nonhomogeneous spatial model of the competition between forest and savanna. We prove that coexistence occurs for a time that is exponential in the size of the system, and that after an initial transient, boundaries between the alternative equilibria remain stable. This result is valid in general for systems that exhibit bistability in a homogeneous environment.