Chris Kuhlman ; Henning Mortveit ; David Murrugarra ; Anil Kumar - Bifurcations in Boolean Networks

dmtcs:2975 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems - https://doi.org/10.46298/dmtcs.2975
Bifurcations in Boolean NetworksArticle

Authors: Chris Kuhlman 1,2; Henning Mortveit 1,3; David Murrugarra 3; Anil Kumar 1,2

  • 1 Network Dynamics and Simulation Science Laboratory
  • 2 Department of Computer Sciences [Blacksburg]
  • 3 Department of Mathematics [Blacksburg]

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.


Volume: DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: bifurcation,bi-threshold,threshold,Boolean networks,graph dynamical systems,synchronous,asynchronous,sequential dynamical systems,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[NLIN.NLIN-CG] Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Collaborative Research: NECO: A Market-Driven Approach to Dynamic Spectrum Sharing; Funder: National Science Foundation; Code: 0831633
  • CAREER: Cross-layer optimization in Cognitive Radio Networks in the Physical interference model based on SINR constraints: Algorithmic Foundations; Funder: National Science Foundation; Code: 0845700
  • Collaborative Research: Modeling Interaction Between Individual Behavior, Social Networks And Public Policy To Support Public Health Epidemiology.; Funder: National Science Foundation; Code: 0729441
  • Collaborative Research: NeTS-NBD: An Integrated Approach to Computing Capacity and Developing Efficient Cross-Layer Protocols for Wireless Networks; Funder: National Science Foundation; Code: 0626964
  • Synthetic Information Systems for Better Informing Public Health Policymakers; Funder: National Institutes of Health; Code: 5U01GM070694-13
  • SDCI NMI New: From Desktops to Clouds -- A Middleware for Next Generation Network Science; Funder: National Science Foundation; Code: 1032677
  • NetSE: Large: Collaborative Research: Contagion in large socio-communication networks; Funder: National Science Foundation; Code: 1011769
  • Tracking the West Antarctic Rift Flank; Funder: National Science Foundation; Code: 0003957
  • Collaborative Research: Coupled Models of Diffusion and Individual Behavior Over Extremely Large Social Networks; Funder: National Science Foundation; Code: 0904844

4 Documents citing this article

Consultation statistics

This page has been seen 347 times.
This article's PDF has been downloaded 247 times.