Dynamics of interdependent critical infrastructures - A mathematical model with unexpected results

Abstract

Abstract The article develops a formal mathematical model which describes the dynamic interactions of interdependent critical infrastructures in discrete time steps, i.e. the direct and indirect consequences (cascading effects) of a disrupted infrastructure to depending infrastructures. The main result here is that a disturbed infrastructure with only a reduced performance level draws (on the long run) all other infrastructures to the same reduced performance level. Also the development of all infrastructures after a full repair of the disturbances is investigated. The related result is that even after a full repair the infrastructures cannot return to full performance without external support. Both results are proved as mathematical theorems. Visualized examples are shown to demonstrate the results.