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Attractors in continuous and Boolean networks

Norell, Johannes; Samuelsson, Björn LU and Socolar, Joshua E. S. (2007) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00 76(4).
Abstract
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of generic continuous systems. We investigate the dynamics in simple rings and rings with one additional self-input. An analysis of switching characteristics and pulse propagation explains the relation between attractors of the continuous systems and their Boolean approximations. For simple rings, “reliable” Boolean attractors correspond to stable continuous attractors. For networks with more complex logic, the qualitative features of continuous attractors are influenced by inherently non-Boolean... (More)
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of generic continuous systems. We investigate the dynamics in simple rings and rings with one additional self-input. An analysis of switching characteristics and pulse propagation explains the relation between attractors of the continuous systems and their Boolean approximations. For simple rings, “reliable” Boolean attractors correspond to stable continuous attractors. For networks with more complex logic, the qualitative features of continuous attractors are influenced by inherently non-Boolean characteristics of switching events. (Less)
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author
publishing date
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
76
issue
4
publisher
American Physical Society
external identifiers
  • scopus:35648994333
ISSN
1539-3755
DOI
10.1103/PhysRevE.76.046122
language
English
LU publication?
no
id
182864cf-5426-4e79-bc19-f42a5584aff2 (old id 1260874)
alternative location
http://link.aps.org/abstract/PRE/v76/e046122
date added to LUP
2008-10-31 09:03:10
date last changed
2017-01-01 04:51:23
@article{182864cf-5426-4e79-bc19-f42a5584aff2,
  abstract     = {We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of generic continuous systems. We investigate the dynamics in simple rings and rings with one additional self-input. An analysis of switching characteristics and pulse propagation explains the relation between attractors of the continuous systems and their Boolean approximations. For simple rings, “reliable” Boolean attractors correspond to stable continuous attractors. For networks with more complex logic, the qualitative features of continuous attractors are influenced by inherently non-Boolean characteristics of switching events.},
  articleno    = {046122},
  author       = {Norell, Johannes and Samuelsson, Björn and Socolar, Joshua E. S.},
  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        = {Attractors in continuous and Boolean networks},
  url          = {http://dx.doi.org/10.1103/PhysRevE.76.046122},
  volume       = {76},
  year         = {2007},
}