Region of attraction estimation of biological continuous Boolean models

M. L. Matthews, C. M. Williams

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Quantitative analysis of biological systems has become an increasingly important research field as scientists look to solve current day health and environmental problems. The development of modeling and model analysis approaches that are specifically geared toward biological processes is a rapidly growing research area. Continuous approximations of Boolean models, for example, have been identified as a viable method for modeling such systems. This is because they are capable of generating dynamic models of biochemical pathways using inferred dependency relationships between components. The resulting nonlinear equations and therefore nonlinear dynamics, however, can present a challenge for most system analysis approaches such as region of attraction (ROA) estimation. Continued progress in the area of biosystems modeling will require that computational techniques used to analyze simple nonlinear systems can still be applied to nonlinear equations typically used to model the dynamics associated with biological processes. In this paper, we assess the applicability of a state of the art ROA estimation technique based on interval arithmetic to a subnetwork of the Rb-E2F signaling pathway modeled using continuous Boolean functions. We show that this method can successfully be used to provide an estimate of the ROA for dynamic models described using Hillcube continuous Boolean approximations.

Original languageEnglish (US)
Title of host publicationProceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
Number of pages6
StatePublished - 2012
Externally publishedYes
Event2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 - Seoul, Korea, Republic of
Duration: Oct 14 2012Oct 17 2012

Publication series

NameConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN (Print)1062-922X


Conference2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
Country/TerritoryKorea, Republic of


  • continuous Boolean modeling
  • Hill functions
  • interval analysis
  • Lyapunov stability
  • region of attraction

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Human-Computer Interaction


Dive into the research topics of 'Region of attraction estimation of biological continuous Boolean models'. Together they form a unique fingerprint.

Cite this