https://doi.org/10.1007/s100510070218
On social percolation and small world network
Mathematics Department,
Faculty of Sciences, UAE University,
Al-Ain, PO Box 17551, Egypt
Mathematics Department,
Faculty of Sciences,
Cairo University,
Giza, Egypt
Corresponding author: a hosny@math-sci.cairo.eun.eg
Received:
24
February
2000
Published online: 15 August 2000
The social percolation model is generalized to include the propagation of two mutually exclusive competing effects on a one-dimensional ring and a two-dimensional square lattice. It is shown that the result depends significantly on which effect propagates first i.e. it is a non-commutative phenomenon. Then the propagation of one effect is studied on a small network. It generalizes the work of Moore and Newman of a disease spread to the case where the susceptibility of the population is random. Three variants of the Domany-Kinzel model are given. One of them (delayed) does not have a chaotic region for some value of the delay weight.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.70.Fh – Phase transitions: general studies / 64.60.Ak – Renormalization-group, fractals, and percolation studies of phase transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
