Critical behavior of propagation on small-world networks

Damián H. Zanette
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a regime where the rumor "dies" in a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the whole population. Critical exponents are evaluated, and the dependence of the critical randomness with the network connectivity is
more » ... onnectivity is studied. The behavior of this system as a function of the small-network randomness bears noticeable similarities with an epidemiological model reported recently [M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)], in spite of substantial differences in the respective dynamical rules.
doi:10.1103/physreve.64.050901 pmid:11735891 fatcat:fprrgy6fufbj7c2eeynrpjsn34