摘要：We introduce a new class of (dynamical) systems that inherently capturecascading effects (viewed as consequential effects) and are naturally amenableto combinations. We develop an axiomatic general theory around those systems,and guide the endeavor towards an understanding of cascading failure. Thetheory evolves as an interplay of lattices and fixed points, and its resultsmay be instantiated to commonly studied models of cascade effects. We characterize the systems through their fixed points, and equip them withtwo operators. We uncover properties of the operators, and express globalsystems through combinations of local systems. We enhance the theory with anotion of failure, and understand the class of shocks inducing a system tofailure. We develop a notion of mu-rank to capture the energy of a system, andunderstand the minimal amount of effort required to fail a system, termedresilience. We deduce a dual notion of fragility and show that the combinationof systems sets a limit on the amount of fragility inherited.
关键词：Mathematics - Combinatorics;Computer Science - Social and Information Networks;Computer Science - Logic in Computer Science;Computer Science - Discrete Mathematics
