Monomials and basin cylinders for network dynamics

Daniel Austin, Ian H. Dinwoodie

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve toward a chosen attractor, for example, initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders, and the other on primary decomposition. Both methods are applied to current examples of gene networks.

Original languageEnglish (US)
Pages (from-to)25-42
Number of pages18
JournalSIAM Journal on Applied Dynamical Systems
Volume14
Issue number1
DOIs
StatePublished - 2015

Keywords

  • Apoptosis
  • Asynchronous network
  • Basin of attraction
  • Boolean network
  • Groebner basis
  • Groebner fan
  • Prime decomposition

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation

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