Canalizing Kauffman networks: non-ergodicity and its effect on their critical behavior

Abstract

Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In particular, we solve the critical condition for systems of units operating according to canalizing functions and present strong numerical evidence that our approach correctly predicts the phase transition from order to chaos in such systems.

arXiv commentto be published in PRL

References in corpus (3)

• Random Boolean Network Models and the Yeast Transcriptional Network
• Emergence of Complex Dynamics in a Simple Model of Signaling Networks
• Lyapunov Exponents in Random Boolean Networks

Cited by in corpus (26)

• Logic and connectivity jointly determine criticality in biological gene regulatory networks
• Boolean nested canalizing functions: a comprehensive analysis
• Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks
• The properties of attractors of canalyzing random Boolean networks
• Evolution of Canalizing Boolean Networks
• Noise in random Boolean networks
• Attractors in continuous and Boolean networks
• Kauffman networks with threshold functions
• The phase diagram of random Boolean networks with nested canalizing functions
• Evolution of a population of random Boolean networks
• Stability of Boolean networks: The joint effects of topology and update rules
• Relevant components in critical random Boolean networks
• Broad edge of chaos in strongly heterogeneous Boolean networks
• Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring
• Robustness, Canalyzing Functions and Systems Design
• Boolean modeling of collective effects in complex networks
• Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
• Influence and Dynamic Behavior in Random Boolean Networks
• Irreversibility in Bacterial Regulatory Networks
• Characterizing short-term stability for Boolean networks over any distribution of transfer functions
• Nested canalizing functions minimize sensitivity and simultaneously promote criticality
• Stratification and enumeration of Boolean functions by canalizing depth
• Interplay between degree and Boolean rules in the stability of Boolean networks
• Self-overlap as a method of analysis in Ising models
• Dynamics of attractor transitions in Boolean networks under noise
• Chaos control in random Boolean networks by reducing mean damage percolation rate