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Title: Damage Spreading in Spatial and Small-world Random Boolean Networks

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 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 non-random 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 relevant component at very low connectivities ($$\bar{K} \ll 1$$) and that the critical connectivity of stability $$K_s$$ changes compared to random networks. At higher $$\bar{K}$$, this scaling remains unchanged. We also show that the relevant component 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 behaviors are obtained by finite-size scaling. 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.
 [1] ;  [2]
  1. Fermilab
  2. Portland State U.
Publication Date:
OSTI Identifier:
Report Number(s):
arXiv:0904.4052; FERMILAB-PUB-14-091-CD
Journal ID: ISSN 1539-3755; 1290092
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics; Journal Volume: 89; Journal Issue: 2
American Physical Society (APS)
Research Org:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States