Equal load-sharing models of cascades in network infrastructures

In recent years, most infrastructures have been exposed to extreme stress due both to the in-creasing demand of services and to an increasing randomness in production and demand. In several of the mostimportant critical infrastructures there is a transported commodity whose flow satisfies conservation laws. Thedynamics on such networks can be described at a first approximation by a linear system of a equations that havethe same structure of Kirchoff equations. We introduce a simplified model of the breakdown behaviour of suchsuch networks under stress and investigate the phenomenon of abrupt breakdown under two scenarios: demandgrowth (mimicking the ever-increasing customer demand) and demand fluctuations (mimicking effects like theone due to renewable sources). Our results indicate that if increasing the system size the heterogeneity of linecapacities increases, the transition becomes more abrupt.