Detecting a prey in a spider orb-web

We consider the inverse problem of localizing a prey hitting a spider orb-web from dynamic measurements taken near the center of the web, where the spider is supposed to stay. The actual discrete orb-web, formed by a finite number of radial and circumferential threads, is modelled as a continuous membrane. The membrane has a specific fibrous structure, which is inherited from the original discrete web, and it is subject to tensile pre-stress in the referential configuration. The transverse load describing the prey's impact is assumed of the form g(t)f(x), where g(t) is a known function of time and f(x) is the unknown term depending on the position variable x. For axially-symmetric orb-webs supported at the boundary and undergoing infinitesimal transverse deformations, we prove a uniqueness result for f(x) in terms of measurements of the transverse dynamic displacement taken on an arbitrarily small and thin ring centered at the origin of the web, for a sufficiently large interval of time. The theoretical result is illustrated by means of a numerical implementation of the identification method.