Vegetation pattern formation and transition in dryland ecosystems with finite soil resources and inertia

The formation of vegetation patterns in dryland ecosystems and the transition between different morphologies are here investigated by means of a bidimensional hyperbolic reaction-transport model. The proposed conceptual framework represents an extension of the classical Klausmeier model in which the finite carrying capacity of the soil and the inertia of biomass and water are also taken into account. The main aim of this work is to elucidate how pattern dynamics occurring at, near and far from the instability threshold are affected by the combined action of limited soil resources, inertia and climate change. To achieve this goal, a threefold investigation is carried out. First, linear stability analysis is addressed to deduce the main pattern features associated with Turing patterns at the onset of instability. Then, multiple-scale weakly nonlinear analysis is employed to characterize the pattern amplitude close to onset. In particular, the study encompasses the description of different pattern morphologies which emerge when the excited eigenmode exhibits single or double multiplicity. Finally, the transition between different patterned states is investigated in far-from-equilibrium conditions, especially to emphasize the nontrivial role played by inertia in the ecosystem response. Numerical simulations are also used to corroborate analytical predictions and to shed light on some key aspects of vegetation pattern dynamics in the context of dryland ecology.