Stability of the Kauffman model.
(2002) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 65(1 Pt 2). p.1016129 Abstract
 Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which removes variables that cannot be relevant to the asymptotic dynamics of the system. The major part of the removed variables have the same fixed state in all limit cycles. These variables are denoted as the stable core of the network and their number grows approximately linearly with N, the number of variables in the original network. The sensitivity of the attractors to perturbations is investigated. We find that reduced networks lack the wellknown insensitivity observed in full Kauffman networks. We conclude that, somewhat counterintuitive, this remarkable property of full Kauffman networks is generated by the dynamics of their... (More)
 Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which removes variables that cannot be relevant to the asymptotic dynamics of the system. The major part of the removed variables have the same fixed state in all limit cycles. These variables are denoted as the stable core of the network and their number grows approximately linearly with N, the number of variables in the original network. The sensitivity of the attractors to perturbations is investigated. We find that reduced networks lack the wellknown insensitivity observed in full Kauffman networks. We conclude that, somewhat counterintuitive, this remarkable property of full Kauffman networks is generated by the dynamics of their stable core. The decimation method is also used to simulate large critical Kauffman networks. For networks up to N=32 we perform full enumeration studies. Strong evidence is provided that the number of limit cycles grows linearly with N. This result is in sharp contrast to the often cited square root of [N] behavior. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/106559
 author
 Bilke, Sven ^{LU} and Sjunnesson, Fredrik ^{LU}
 organization
 publishing date
 2002
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
 volume
 65
 issue
 1 Pt 2
 pages
 1  016129
 publisher
 American Physical Society
 external identifiers

 wos:000173407500040
 scopus:41349121540
 pmid:11800758
 ISSN
 15393755
 DOI
 10.1103/PhysRevE.65.016129
 language
 English
 LU publication?
 yes
 id
 54b0915e59804284b3a4c23c3ae89338 (old id 106559)
 alternative location
 http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11800758&dopt=Abstract
 date added to LUP
 20160401 12:01:52
 date last changed
 20201208 04:03:19
@article{54b0915e59804284b3a4c23c3ae89338, abstract = {Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which removes variables that cannot be relevant to the asymptotic dynamics of the system. The major part of the removed variables have the same fixed state in all limit cycles. These variables are denoted as the stable core of the network and their number grows approximately linearly with N, the number of variables in the original network. The sensitivity of the attractors to perturbations is investigated. We find that reduced networks lack the wellknown insensitivity observed in full Kauffman networks. We conclude that, somewhat counterintuitive, this remarkable property of full Kauffman networks is generated by the dynamics of their stable core. The decimation method is also used to simulate large critical Kauffman networks. For networks up to N=32 we perform full enumeration studies. Strong evidence is provided that the number of limit cycles grows linearly with N. This result is in sharp contrast to the often cited square root of [N] behavior.}, author = {Bilke, Sven and Sjunnesson, Fredrik}, issn = {15393755}, language = {eng}, number = {1 Pt 2}, pages = {1016129}, publisher = {American Physical Society}, series = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, title = {Stability of the Kauffman model.}, url = {http://dx.doi.org/10.1103/PhysRevE.65.016129}, doi = {10.1103/PhysRevE.65.016129}, volume = {65}, year = {2002}, }