Dynamics of Boolean networks - an exact solution

Abstract

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.

References in corpus (4)

• The phase diagram of random threshold networks
• Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions
• Noise in random Boolean networks
• Redundancy and error resilience in Boolean Networks

Cited by in corpus (9)

• Impact of individual nodes in Boolean network dynamics
• Stability of Boolean networks: The joint effects of topology and update rules
• Dynamical Instability in Boolean Networks as a Percolation Problem
• The matrix product approximation for the dynamic cavity method
• Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise
• Characterizing short-term stability for Boolean networks over any distribution of transfer functions
• The behavior of noise-resilient Boolean networks with diverse topologies
• Phase transitions and memory effects in the dynamics of Boolean networks
• Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise