On social percolation and small world network

The social percolation model is generalized to include the propagation of t wo mutually exclusive competing effects on a one-dimensional ring and a two -dimensional square lattice. It is shown that the result depends significan tly on which effect propagates first i.e. it is a non-commutative phenomeno n. Then the propagation of one effect is studied on a small network. It gen eralizes 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 Doma ny-Kinzel model are given. One of them (delayed) does not have a chaotic re gion for some value of the delay weight.