A minimal model of interaction between climate and vegetation: qualitative approach

A so-called “minimal model” is presented for the qualitative description of the interaction between climate and vegetation. Such conceptual simple models are important to give a better understanding of the fundamental feedback mechanisms acting between geo- and biosphere. This spatially one-dimensional model is analyzed in respect to the uniform biosphere and the existence of possible diffusive instabilities. It is proved that there do not exist any non-uniform equilibrium solutions, but the evolution of non-uniform initial perturbations is quite interesting: depending on the spatial form of the perturbations propagating non-linear waves are observed.