Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model

Abstract

We consider a generic interaction-redistribution model of vegetation dynamics to investigate the formation of patchy vegetation in semi-arid and arid landscapes. First, we perform a weakly nonlinear analysis in the neighborhood of the symmetry-breaking instability. Following this analysis, we construct the bifurcation diagram of the biomass density. The weakly nonlinear analysis allows us to establish the condition under which the transition from super- to subcritical symmetry-breaking instability takes place. Second, we generate a random distribution of localized patches of vegetation numerically. This behavior occurs in regimes where a bare state coexists with a uniform biomass density. Field observations allow to estimate the total biomass density and the range of facilitative and competitive interactions.