2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/83317We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to a homogeneous state or nucleating a pair of oppositely moving fronts. The corresponding bifurcation diagram demonstrates a cusp singularity. The obtained analytic results are in good quantitative agreement with numerical simulations.4 pages, 5 figures, revtexPattern Formation and Solitonstext