Damage Spreading and Criticality in Finite Random Dynamical Networks

Abstract

We systematically study and compare damage spreading at the sparse percolation (SP) limit for random boolean and threshold networks with perturbations that are independent of the network size $N$. This limit is relevant to information and damage propagation in many technological and natural networks. Using finite size scaling, we identify a new characteristic connectivity $K_s$, at which the average number of damaged nodes $\bar{d}$, after a large number of dynamical updates, is independent of $N$. Based on marginal damage spreading, we determine the critical connectivity $K_c^{sparse}(N)$ for finite $N$ at the SP limit and show that it systematically deviates from $K_c$, established by the annealed approximation, even for large system sizes. Our findings can potentially explain the results recently obtained for gene regulatory networks and have important implications for the evolution of dynamical networks that solve specific computational or functional tasks.

4 pages, 4 eps figures

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Cited by in corpus (11)

• Colloquium: Criticality and dynamical scaling in living systems
• The effect of the forget-remember mechanism on spreading
• Computational Capabilities of Random Automata Networks for Reservoir Computing
• Emergent Criticality Through Adaptive Information Processing in Boolean Networks
• Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring
• Stability of Boolean and continuous dynamics
• Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
• Assessing Random Dynamical Network Architectures for Nanoelectronics
• Evolution of regulatory networks towards adaptability and stability in a changing environment
• Kauffman Boolean model in undirected scale free networks
• Critical line in undirected Kauffman boolean networks - the role of percolation