On a framework for analysis and design of cascades on Boolean networks

Griffin Kearney, Makan Fardad

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We consider Boolean networks defined on directed graphs in which the state of every node belongs to the set {0; 1}. We think of a node in state 1 as having 'failed'. The state of every node at the next time instant is a function of the states of those nodes that link to it. Nodes fail according to a set of rules, and once a node fails it stays so forever. We develop a mathematical framework that allows us to find the smallest set of nodes whose failure at time zero causes the eventual failure of all nodes in a desired target set. Our methods are based on modeling network dynamics using Boolean polynomials and exploiting their properties. Rather than propagating the state forward using a nonlinear map, we characterize all possible steady-state configurations as the fixed points of the network's dynamics, and provide a simple algorithm for finding all such 'stable' configurations. We demonstrate the utility of our framework with the help of illustrative examples.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages997-1002
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

Keywords

  • Boolean networks
  • Boolean polynomials
  • cascading failures

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

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  • Cite this

    Kearney, G., & Fardad, M. (2016). On a framework for analysis and design of cascades on Boolean networks. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 997-1002). [7798398] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798398