Online at stacks.iop.org/Non/17/23

An analysis of front dynamics in discrete time and spatially extended systems with general bistable nonlinearity is presented. The spatial coupling is given by the convolution with distribution functions. It allows us to treat in a unified way discrete, continuous or partly discrete and partly continuous diffusive interactions. We prove the existence of fronts and the uniqueness of their velocity. We also prove that the front velocity depends continuously on the parameters of the system. Finally, we show that every initial configuration that is an interface between the stable phases propagates asymptotically with the front velocity. Mathematics Subject Classification: 37L99, 39B22, 46T20 1. Systems of bistable maps coupled by convolutions Fronts between two stable phases is a widespread phenomenon in spatially extended systems. Such nonlinear waves are believed to emerge in the presence of a bistable nonlinearity and a diffusive coupling. In particular, they should manifest themselves independently of the discret