Pattern formation and numerical bifurcation analysis for a vegetation model

Several mathematical models were formulated as systems of PDEs to simulate vegetation patterns. These vegetation patterns are observed in numerous regions around the world ( [1]) and it has been hypothesized that their development is affected by global phenomena like climate change ( [1]). These mathematical models that has been used to simulate the vegetation pattern formation consider positive feedback mechanisms between water and biomass. Moreover, some studies explain pattern formation as a consequence of negative plant-soil feedback interactions. In this work we present a pattern formation and a numerical bifurcation analysis of a vegetation model which includes negative plant-soil feedback, based on the PDE model of [3]. The study has revealed the existence of variety of different spatial patterns in the space arising from Turing bifurcation of the homogeneous state. The effect of the precipitation rate is analyzed as system parameter. Coexistence between different patterns has been observed in a wide range of precipitation rate. Moreover the effect of boundary conditions on the nonlinear dynamics is also discussed