Quantifying stability…, J. Kurths. The dynamics of complex networks, e.g. evolving networks where the connectivity is not constant in time. One is interested e.g. in failure in power grids, “monster blackouts” (e.g. India, July 31, 2012, > 620 Millions people without electricity) due to cascading effects. He wants to study these problems in the light of stability of dynamical systems. An example is to study a network of N identical oscillators. Is it possible to synchronize in the whole network*. There exist some criteria (Pecora & Carrol 1998) which can be applied to special kind of networks (e.g. small-world) [see also Rossler oscillators]. It happens that the most synchronizable network are the more random. One then wants to study the “basin of attraction” of a network of oscillators [Nature Physics 9, 89]. He also mentioned the Kuramoto model for power grids, and applied it to real networks like the Scandinavian power grid.
* Synchronization in networks might be related to fundamental cycles! Because synchronization on a tree should always be possible.