Skip to Main content Skip to Navigation
Conference papers

Bifurcations in Boolean Networks

Abstract : This paper characterizes the attractor structure of synchronous and asynchronous Boolean networks induced by bi-threshold functions. Bi-threshold functions are generalizations of standard threshold functions and have separate threshold values for the transitions $0 \rightarrow $1 (up-threshold) and $1 \rightarrow 0$ (down-threshold). We show that synchronous bi-threshold systems may, just like standard threshold systems, only have fixed points and 2-cycles as attractors. Asynchronous bi-threshold systems (fixed permutation update sequence), on the other hand, undergo a bifurcation. When the difference $\Delta$ of the down- and up-threshold is less than 2 they only have fixed points as limit sets. However, for $\Delta \geq 2$ they may have long periodic orbits. The limiting case of $\Delta = 2$ is identified using a potential function argument. Finally, we present a series of results on the dynamics of bi-threshold systems for families of graphs.
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download

https://hal.inria.fr/hal-01196142
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, September 9, 2015 - 11:15:02 AM
Last modification on : Wednesday, April 10, 2019 - 2:18:02 PM
Long-term archiving on: : Monday, December 28, 2015 - 11:02:02 PM

File

dmAP0103.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01196142, version 1

Collections

Citation

Chris Kuhlman, Henning Mortveit, David Murrugarra, Anil Kumar. Bifurcations in Boolean Networks. 17th International Workshop on Celular Automata and Discrete Complex Systems, 2011, Santiago, Chile. pp.29-46. ⟨hal-01196142⟩

Share

Metrics

Record views

232

Files downloads

863