Physics (Internal)

Spontaneous Recovery in Dynamical Networks

This event is part of the Preliminary Oral Exam.

Examining Committee: H.E. Stanley, Shlomo Havlin, Lawrence Sulak, William Skocpol

Abstract:

Many things around us interact and are connected. While we have a very good understanding of interactions between elementary particles, atoms or molecules, it is a difficult task to describe and understand interactions between individual units in complex systems that we find in biology, society, finance, Internet, infrastructure, traffic, and many others. In the last decade, physicists working on complex networks have been very much focused on various kinds of spreading phenomena (damage spreading, transport, activation processes), since these yield phenomena well known in physics - phase transitions are most notable example. Of particular interest are abrupt dynamic events that cause networks to irreversibly fail. However, a remarkable property of many real-world networks is that they can sometimes recover spontaneously after they collapse—think of traffic jams suddenly easing, sudden market crashes followed by recoveries, or people waking from a coma. In some systems such as financial markets or traffic networks, failures and recoveries are a never-ending sequence. To model this marked network recovery, we examine the effect of local node recoveries and stochastic contiguous spreading, and find that they can lead to the spontaneous emergence of macroscopic ‘phase-flipping’ phenomena. As the network is of finite size and is stochastic, the fraction of active nodes z switches back and forth between the two network collective modes characterized by high network activity and low network activity. Furthermore, the system exhibits a strong hysteresis behaviour analogous to phase transitions near a critical point. To explain the phase-flipping phenomena fundamentally, we develop a picture (representation) of the underlying mechanism as the first passage process in the hysteresis region of the phase diagram. We present real-world network data that suggest switching behaviour in accord with the predictions of the model.