Damage Spreading in Spatial and Small-world Random Boolean Networks

Journal Article · Tue Feb 18 00:00:00 EST 2014 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.89.022806· OSTI ID:1289769

Lu, Qiming ^[1]; Teuscher, Christof ^[2]

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1. Fermilab
2. Portland State U.

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.

• Research Organization: Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• DOE Contract Number: AC02-07CH11359
• OSTI ID: 1289769
• Report Number(s): arXiv:0904.4052; FERMILAB-PUB-14-091-CD; 1290092
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 89, Issue 2; ISSN 1539-3755
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English