Localized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving release_vtlklhkg6zbxngank2mjy46o6i

Abstract

We 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.
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