Complex spatiotemporal patterns in two lattice models with instability

In this paper we consider two lattice models: (i) the discretized version of a simple nonlinear partial differential equation (PDE) with a singular term and (ii) a coupled map lattice (CML) with unstable coupling. Both systems are defined by simple iteration rules involving the nearest-neighbour grid points of the corresponding one-dimensional lattice. We show numerically that these models result in an apparently stochastic spatiotemporal behaviour and exhibit interesting regimes as the function of the parameters of the models. In particular, we find that by varying the relative weight B of the singular term in the PDE the total width of the solution scales with B. The CML leads to an intermittent behaviour between structured and turbulent regimes