The phase diagram of random threshold networks

Abstract

Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behaviour with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold networks with real-valued thresholds h and a fixed number of inputs per node. The nodes are updated according to the same rules as in a model of the cell-cycle network of Saccharomyces cereviseae [PNAS 101, 4781 (2004)]. Using the annealed approximation, we derive expressions for the time evolution of the proportion of nodes in the "on" and "off" state, and for the sensitivity $\lambda$. The results are compared with simulations of quenched networks. We find that for integer values of h the simulations show marked deviations from the annealed approximation even for large networks. This can be attributed to the particular choice of the updating rule.

8 pages, 6 figures

References in corpus (3)

• The Yeast Cell-Cycle Network Is Robustly Designed
• Criticality in Random Threshold Networks: Annealed Approximation and Beyond
• Scaling in critical random Boolean networks

Cited by in corpus (16)

• Signal integration enhances the dynamic range in neuronal systems
• Noise in random Boolean networks
• Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks
• Impact of individual nodes in Boolean network dynamics
• Binary threshold networks as a natural null model for biological networks
• The phase diagram of random Boolean networks with nested canalizing functions
• Stability of Boolean networks: The joint effects of topology and update rules
• Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
• Influence and Dynamic Behavior in Random Boolean Networks
• Dynamics of Boolean networks - an exact solution
• Critical excitation-inhibition balance in dense neural networks
• The behavior of noise-resilient Boolean networks with diverse topologies
• Prediction of lethal and synthetically lethal knock-outs in regulatory networks
• Phase transitions and memory effects in the dynamics of Boolean networks
• Predicting attractors from spectral properties of stylized gene regulatory networks
• Are Genetically Robust Regulatory Networks Dynamically Different from Random Ones?