Percolation, Cascades, and Control of Networks
This event is part of the Physics Department Colloquia Series.
Networks are at the core of modern society, spanning physical, biological and social systems. Each distinct network is typically a complex system, shaped by the collective action of individual agents and displaying emergent behaviors. Moreover, collections of these complex networks often interact and depend upon one another, which can lead to unanticipated consequences such as cascading failures and novel phase transitions. Simple mathematical models of networks, grounded in techniques from statistical physics, can provide important insights into such phenomena. Here we will cover several such models, beginning with control of phase transitions in an individual network and the novel classes of percolation phase transitions that result from repeated, small interventions intended to delay the transition. We then move on to modeling phenomena in coupled networks, including cascading failures and the notion of optimal interdependence. Finally, we focus on abrupt transitions due to a system jumping between bi-stable equilibrium, and show that when such systems interact we can observe a new phenomena of catastrophe-hopping leading to non-local cascading failures. Here an intermediate system facilitates the propagation of a sudden change or collapse, and we show that catastrophe hopping is consistent with the outbreak of protests observed during the Arab Spring of 2011.