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 most important critical infrastructures there is a transported commodity whose flow satisfies conservation laws. The dynamics on such networks can be described at a first approximation by a linear system of a equations that have the same structure of Kirchoff equations. We introduce a simplified model of the breakdown behaviour of such such networks under stress and investigate the phenomenon of abrupt breakdown under two scenarios: demand growth (mimicking the ever-increasing customer demand) and demand fluctuations (mimicking effects like the one due to renewable sources). Our results indicate that if increasing the system size the heterogeneity of line capacities increases, the transition becomes more abrupt.