A SHOT-NOISE APPROACH TO DECAY/SURGE COLLECTIVE POPULATION MODELS

Shot-noise models deals with the cumulative output of a system whose input is subject to a random Poisson succession of equally distributed impulses or shots, each followed by some attenuation dynamics. With population dynamics in mind, we study the cases when the attenuation dynamics is either given by some ad hoc attenuation function or by some nonlinear ordinary dynamical system or by a (sub-)critical branching process. In the three cases, an interesting issue concerning extinction and idle periods is when the subpopulations can go extinct in finite time.