The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

Profile picture. Photo.

Carl Troein

Researcher

Profile picture. Photo.

Random maps and attractors in random Boolean networks

Author

  • Björn Samuelsson
  • Carl Troein

Summary, in English

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.

Department/s

  • Computational Biology and Biological Physics - Undergoing reorganization
  • Functional zoology

Publishing year

2005

Language

English

Publication/Series

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Volume

72

Issue

4

Document type

Journal article

Publisher

American Physical Society

Topic

  • Zoology
  • Biophysics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1539-3755