The prey's catching problem in an elastically supported spider orb-web

Spiders use their orb-web not only to capture prey, but also as a sensor to detect the position of the area where it has impacted. The web, serving as a waveguide, transmits to its eight legs the vibratory information so that the spider can orient itself towards the prey, performing a task similar to solving an inverse problem. Although the response of spiders to vibrations has been studied for over 100 years, the understanding of the dynamic response of the web and its ability to serve as a sensor remains largely incomplete. Some recent work has made significant progress in this area, in particular in the formulation of the catching problem as an inverse problem (Kawano and Morassi [1,2]), using a continuous membrane model for the orb-web (Morassi et al. [3]). Here, we continue this line of research by relaxing the condition of null displacement at the boundary of the web (rigid support) that was considered in previous studies, thus approaching the reality of a not necessarily rigid substrate (e.g., leaves) to which spiders anchor their web. The creation of a reconstruction algorithm for identifying the load support provides an answer to the inverse problem. Additionally, the adoption of the support stiffness as a fundamental parameter of the study allows the analysis of its influence on the quality of the identification.