Search results for "inertial time"
showing 3 items of 3 documents
Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal
2022
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 solution…
Pattern formation in hyperbolic reaction-transport systems and applications to dryland ecology
2023
Pattern formation and modulation is an active branch of mathematics, not only from the perspective of fundamental theory but also for its huge applications in many fields of physics, ecology, chemistry, biology, and other sciences. In this thesis, the occurrence of Turing and wave instabilities, giving rise to stationary and oscillatory patterns, respectively, is theoretically investigated by means of two-compartment reaction-transport hyperbolic systems. The goal is to elucidate the role of inertial times, which are introduced in hyperbolic models to account for the finite-time propagation of disturbances, in stationary and transient dynamics, in supercritical and subcritical regimes. In p…
Vegetation Patterns in the Hyperbolic Klausmeier Model with Secondary Seed Dispersal
2023
This work focuses on the dynamics of vegetation stripes in sloped semi-arid environments in the presence of secondary seed dispersal and inertial effects. To this aim, a hyperbolic generalization of the Klausmeier model that encloses the advective downhill transport of plant biomass is taken into account. Analytical investigations were performed to deduce the wave and Turing instability loci at which oscillatory and stationary vegetation patterns arise, respectively. Additional information on the possibility of predicting a null-migrating behavior was extracted with suitable approximations of the dispersion relation. Numerical simulations were also carried out to corroborate theoretical pre…