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Random maps and attractors in random Boolean networks

Samuelsson, Björn LU and Troein, Carl LU (2005) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00 72(4).
Abstract
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per node can be seen as graphs of random maps. We introduce an approach to investigating random maps and finding analytical results for attractors in random Boolean networks with the corresponding topology. Approximating some other non-chaotic networks to be of this class, we apply the analytic results to them. For this approximation, we observe a strikingly good agreement on the numbers of attractors of various lengths. We also investigate observables related to the average number of attractors in relation... (More)
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per node can be seen as graphs of random maps. We introduce an approach to investigating random maps and finding analytical results for attractors in random Boolean networks with the corresponding topology. Approximating some other non-chaotic networks to be of this class, we apply the analytic results to them. For this approximation, we observe a strikingly good agreement on the numbers of attractors of various lengths. We also investigate observables related to the average number of attractors in relation to the typical number of attractors. Here, we find strong differences that highlight the difficulties in making direct comparisons between random Boolean networks and real systems. Furthermore, we demonstrate the power of our approach by deriving some results for random maps. These results include the distribution of the number of components in random maps, along with asymptotic expansions for cumulants up to the fourth order. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00
volume
72
issue
4
publisher
American Physical Society
external identifiers
  • wos:000232931200024
  • scopus:33244476083
ISSN
1539-3755
DOI
10.1103/PhysRevE.72.046112
language
English
LU publication?
yes
id
029b6342-480f-4670-bf31-aa53be1dedfb (old id 214150)
alternative location
http://link.aps.org/abstract/PRE/v72/e046112
date added to LUP
2007-08-23 17:40:03
date last changed
2017-08-27 04:01:13
@article{029b6342-480f-4670-bf31-aa53be1dedfb,
  abstract     = {Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per node can be seen as graphs of random maps. We introduce an approach to investigating random maps and finding analytical results for attractors in random Boolean networks with the corresponding topology. Approximating some other non-chaotic networks to be of this class, we apply the analytic results to them. For this approximation, we observe a strikingly good agreement on the numbers of attractors of various lengths. We also investigate observables related to the average number of attractors in relation to the typical number of attractors. Here, we find strong differences that highlight the difficulties in making direct comparisons between random Boolean networks and real systems. Furthermore, we demonstrate the power of our approach by deriving some results for random maps. These results include the distribution of the number of components in random maps, along with asymptotic expansions for cumulants up to the fourth order.},
  articleno    = {046112},
  author       = {Samuelsson, Björn and Troein, Carl},
  issn         = {1539-3755},
  language     = {eng},
  number       = {4},
  publisher    = {American Physical Society},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00},
  title        = {Random maps and attractors in random Boolean networks},
  url          = {http://dx.doi.org/10.1103/PhysRevE.72.046112},
  volume       = {72},
  year         = {2005},
}