title: Damage spreading in spatial and small-world random Boolean networks.
abstract: The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean networks (RBNs) are commonly used as a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other nonrandom connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the Hamming distance at very low connectivities (K ≪ 1) and that the critical connectivity of stability K(s) changes compared to random networks. At higher K, this scaling remains unchanged. We also show that the Hamming distance of spatially local networks scales with a power law as the system size N increases, but with a different exponent for local and small-world networks. The scaling arguments for small-world networks are obtained with respect to the system sizes and strength of spatially local connections. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.
authors.affiliation: Scientific Computing Division, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-5011, USA.
authors.forename: Qiming
authors.initials: Q
authors.lastname: Lu
authors.affiliation: Department of Electrical and Computer Engineering (ECE), Portland State University, P.O. Box 751, Portland, Oregon 97207-0751, USA.
authors.forename: Christof
authors.initials: C
authors.lastname: Teuscher
mesh_terms: D000465:Algorithms; D000818:Animals; D003195:Computer Communication Networks / Q000706:statistics & numerical data*; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*