Effects of local nonlinearity and basin size in the dynamics of lattices of bistable maps

We investigate the propagation of bistable fronts in lattices of diffusively and advectively coupled cubic and quartic bistable maps, reporting the distribution of both stable states for asymmetric basins of attraction. The main effects of basin symmetry and local nonlinearities are obtained by comparing distributions for cubic local dynamics, with either symmetric or asymmetric basins of attraction, with those obtained for quartic maps with asymmetric basins. In addition, we show how front velocities depend on the local parameter and diffusion.