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Exhaustive percolation on random networks.

Publication ,  Journal Article
Samuelsson, B; Socolar, JES
Published in: Physical review. E, Statistical, nonlinear, and soft matter physics
September 2006

We consider propagation models that describe the spreading of an attribute, called "damage," through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a phenomenon we refer to as exhaustive percolation. We derive scaling law exponents and exact results for the distribution of the number of undamaged nodes, valid for a broad class of random networks at the exhaustive percolation transition and in the exhaustive percolation regime. This class includes processes that determine the set of frozen nodes in random Boolean networks with in-degree distributions that decay sufficiently rapidly with the number of inputs. Connections between our calculational methods and previous studies of percolation beginning from a single initial node are also pointed out. Central to our approach is the observation that key aspects of damage spreading on a random network are fully characterized by a single function, specifying the probability that a given node will be damaged as a function of the fraction of damaged nodes. In addition to our analytical investigations of random networks, we present a numerical example of exhaustive percolation on a directed lattice.

Duke Scholars

Published In

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

September 2006

Volume

74

Issue

3 Pt 2

Start / End Page

036113

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Samuelsson, B., & Socolar, J. E. S. (2006). Exhaustive percolation on random networks. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 74(3 Pt 2), 036113. https://doi.org/10.1103/physreve.74.036113
Samuelsson, Björn, and Joshua E. S. Socolar. “Exhaustive percolation on random networks.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 74, no. 3 Pt 2 (September 2006): 036113. https://doi.org/10.1103/physreve.74.036113.
Samuelsson B, Socolar JES. Exhaustive percolation on random networks. Physical review E, Statistical, nonlinear, and soft matter physics. 2006 Sep;74(3 Pt 2):036113.
Samuelsson, Björn, and Joshua E. S. Socolar. “Exhaustive percolation on random networks.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 74, no. 3 Pt 2, Sept. 2006, p. 036113. Epmc, doi:10.1103/physreve.74.036113.
Samuelsson B, Socolar JES. Exhaustive percolation on random networks. Physical review E, Statistical, nonlinear, and soft matter physics. 2006 Sep;74(3 Pt 2):036113.

Published In

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

September 2006

Volume

74

Issue

3 Pt 2

Start / End Page

036113

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences