Pattern formation in hyperbolic reaction-transport systems and applications to dryland ecology

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…