Localized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving

Igor Mitkov; Konstantin Kladko; A. R. Bishop

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arXiv · patt-sol/9812008

Localized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving

Igor Mitkov·Konstantin Kladko·A. R. Bishop

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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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Igor Mitkov, Konstantin Kladko, A. R. Bishop. 1998-12-23. Localized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving. https://arxiv.org/abs/patt-sol/9812008

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