Mathematics – Dynamical Systems
Scientific paper
2010-12-29
Mathematics
Dynamical Systems
19th International Symposium on Mathematical Theory of Networks and Systems, Budapest, Hungary, 5-9 July 2010
Scientific paper
Large, complex networks are ubiquitous in nature and society, and there is great interest in developing rigorous, scalable methods for identifying and characterizing their vulnerabilities. This paper presents an approach for analyzing the dynamics of complex networks in which the network of interest is first abstracted to a much simpler, but mathematically equivalent, representation, the required analysis is performed on the abstraction, and analytic conclusions are then mapped back to the original network and interpreted there. We begin by identifying a broad and important class of complex networks which admit vulnerability-preserving, finite state abstractions, and develop efficient algorithms for computing these abstractions. We then propose a vulnerability analysis methodology which combines these finite state abstractions with formal analytics from theoretical computer science to yield a comprehensive vulnerability analysis process for networks of realworld scale and complexity. The potential of the proposed approach is illustrated with a case study involving a realistic electric power grid model and also with brief discussions of biological and social network examples.
Colbaugh Richard
Glass Kristin
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