Criticality in Random Threshold Networks: Annealed Approximation and Beyond

Abstract

Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of model - contrary to Boolean Networks - propagation of local perturbations (damage) depends on the in-degree of the sites. $K_c$ is determined analytically, using an annealed approximation, and the results are confirmed by numerical simulations. It is shown that the statistical distributions of damage spreading near the percolation transition obey power-laws, and dynamical correlations between active network clusters become maximal. We investigate the effect of local damage suppression at highly connected nodes for networks with scale-free in-degree distributions. Possible relations of our findings to properties of real-world networks, like robustness and non-trivial degree-distributions, are discussed.

8 pages RevTeX, 8 figures PostScript

References in corpus (1)

• Lethality and centrality in protein networks

Cited by in corpus (20)

• Colloquium: Criticality and dynamical scaling in living systems
• Rapid Time Series Prediction with a Hardware-Based Reservoir Computer
• Damage Spreading and Criticality in Finite Random Dynamical Networks
• Chaotic Gene Regulatory Networks Can Be Robust Against Mutations and Noise
• The phase diagram of random threshold networks
• Binary threshold networks as a natural null model for biological networks
• Kauffman networks with threshold functions
• The phase diagram of random Boolean networks with nested canalizing functions
• Emergence of geometric Turing patterns in complex networks
• Stability of Boolean networks: The joint effects of topology and update rules
• Threshold cascade dynamics on signed random networks
• Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring
• Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
• Boolean networks with veto functions
• Morphogenesis by coupled regulatory networks: Reliable control of positional information and proportion regulation
• Assessing Random Dynamical Network Architectures for Nanoelectronics
• A characterization of the Edge of Criticality in Binary Echo State Networks
• Critical excitation-inhibition balance in dense neural networks
• Nested canalizing functions minimize sensitivity and simultaneously promote criticality
• Ashkin-Teller model with antiferromagnetic four-spin interactions: Interference effect between two conflicting issues