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On social percolation and small world network |
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| Authors: | E. Ahmed H.A. Abdusalam |
| Affiliation: | (1) Mathematics Department, Faculty of Sciences, UAE University, Al-Ain, PO Box 17551, Egypt, EG;(2) Mathematics Department, Faculty of Sciences, Cairo University, Giza, Egypt, EG |
| Abstract: | 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. Received 24 February 2000 |
| Keywords: | 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 |
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