title: Stability of Boolean networks: the joint effects of topology and update rules.
abstract: We study the stability of orbits in large Boolean networks. We treat the case in which the network has a given complex topology, and we do not assume a specific form for the update rules, which may be correlated with local topological properties of the network. While recent past work has addressed the separate effects of complex network topology and certain classes of update rules on stability, only crude results exist about how these effects interact. We present a widely applicable solution to this problem. Numerical simulations confirm our theory and show that local correlations between topology and update rules can have profound effects on the qualitative behavior of these systems.
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland, USA and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland, USA.
authors.forename: Shane
authors.initials: S
authors.lastname: Squires
authors.affiliation: Potomac Research, LLC, Alexandria, Virginia, USA.
authors.forename: Andrew
authors.initials: A
authors.lastname: Pomerance
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland, USA and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland, USA and Institute for the Physical Sciences and Technology, University of Maryland, College Park, Maryland, USA.
authors.forename: Michelle
authors.initials: M
authors.lastname: Girvan
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland, USA and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland, USA and Department of Electrical Engineering, University of Maryland, College Park, Maryland, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Ott
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical