Exhaustive percolation on random networks
(2006) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 74(3). Abstract
 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 indegree distributions that decay sufficiently rapidly with the number of inputs. Connections between our calculational methods... (More)
 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 indegree 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1260848
 author
 Samuelsson, Björn ^{LU} and Socolar, Joshua E. S.
 publishing date
 2006
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
 volume
 74
 issue
 3
 publisher
 American Physical Society
 external identifiers

 scopus:33749244629
 ISSN
 15393755
 DOI
 10.1103/PhysRevE.74.036113
 language
 English
 LU publication?
 no
 id
 5c8050c08dd54d36bed7bc130725be1f (old id 1260848)
 alternative location
 http://link.aps.org/abstract/PRE/v74/e036113
 date added to LUP
 20081031 09:02:57
 date last changed
 20190730 01:49:51
@article{5c8050c08dd54d36bed7bc130725be1f, abstract = {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 indegree 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.}, articleno = {036113}, author = {Samuelsson, Björn and Socolar, Joshua E. S.}, issn = {15393755}, language = {eng}, number = {3}, publisher = {American Physical Society}, series = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, title = {Exhaustive percolation on random networks}, url = {http://dx.doi.org/10.1103/PhysRevE.74.036113}, volume = {74}, year = {2006}, }