Power networks and collaborating mobile robots are examples of large-scale interdependent systems that are subject to cascading failures. A recent asymptotic model of failure across two signal domains offers a random graph framework for studying such systems, and I use it to pose and solve a new robust design problem. A low-order nonlinear analysis uncovers the mechanisms by which optimized graphs can form star-like clusters, as encoded into a simple but specialized degree distribution; several other design rules can be found as well. Through examples on coupled systems of finite size, I show that degree independence in the asymptotic model can be somewhat relaxed, which is significant for the practical case of geometric connectivity. A heuristic rule that matches degrees across the domain boundary can offer further benefits in many cases.
Monday, February 14, 2011
Free and open to the public