Omori law after exogenous shocks on supplier-customer network

Abstract

We study the relaxation process of a supplier-customer network after mass destruction due to two giant earthquakes, Kobe 1995 and East Japan 2011, by investigating the number of chained failures. Firstly, a mass destruction and intervention of business activities in the damaged areas can be considered as a main shock. The exogenous shock was propagated on the supplier-customer network deteriorating financial states of other firms, even if they are not located in geographical neighbors. To quantify such aftershocks, we use chained failures on the network assuming that they indicate the trace of propagation of shocks. We show that the number of chained failures in its temporal change obeys an Omori-law, a power-law relaxation. This finding implies that the relaxation is much more sluggish than one would naively expect, and that it might be possible to estimate the extent and duration of aftershocks by using the empirical law. Several issues are discussed including the origin of the long-time relaxation. © Springer-Verlag Italia 2013.