Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal

This manuscript tackles the study of vegetation pattern dynamics driven by inertial effects and secondary seed dispersal. To achieve this goal, an hyperbolic extension of the classical parabolic Klausmeier model of vegetation, generally used to predict the formation of banded vegetation along the slopes of semiarid environments, has been here considered together with an additional advective term mimicking the downslope motion of seeds. Linear stability analyses have been carried out to inspect the dependence of the wave instability locus on the model parameters, with particular emphasis on the role played by inertial time and seed advection speed. Moreover, periodic travelling wave solutions are taken into account to better characterize modulus and direction of the migration speed of striped vegetation patterns. Theoretical predictions are corroborated by numerical Investigations and ecological implications are also discussed. In particular, it is highlighted how the hyperbolic nature of the model may provide possible justifications about some controversial field observations.