Thresholds and Complex Dynamics of Interdependent Cascading Infrastructure Systems

Critical infrastructures have a number of the characteristic properties of complex systems. Among these are infrequent large failures through cascading events. These events, though infrequent, often obey a power law distribution in their probability versus size which suggests that conventional risk analysis does not apply to these systems. Real infrastructure systems typically have an additional layer of complexity, namely the heterogeneous coupling to other infrastructure systems that can allow a failure in one system to propagate to the other system. Here, we model the infrastructure systems through a network with complex system dynamics. We use both mean field theory to get analytic results and a numerical complex systems model, Demon, for computational results. An isolated system has bifurcated fixed points and a cascading threshold which is the same as the bifurcation point. When systems are coupled, this is no longer true and the cascading threshold is different from the bifurcation point of the fixed point solutions. This change in the cascading threshold caused by the interdependence of the system can have an impact on the “safe operation” of interdependent infrastructure systems by changing the critical point and even the power law exponent.