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)
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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/214150
- author
- Samuelsson, Björn
LU
and Troein, Carl
LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
- volume
- 72
- issue
- 4
- article number
- 046112
- publisher
- American Physical Society
- external identifiers
-
- wos:000232931200024
- scopus:33244476083
- pmid:16383473
- 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
- 2016-04-01 12:01:56
- date last changed
- 2024-03-25 22:24:49
@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.}},
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)}},
title = {{Random maps and attractors in random Boolean networks}},
url = {{http://dx.doi.org/10.1103/PhysRevE.72.046112}},
doi = {{10.1103/PhysRevE.72.046112}},
volume = {{72}},
year = {{2005}},
}