Fronts Between Periodic Patterns for Bistable Recursions on Lattices



Bistable space–time discrete systems commonly possess a large variety of stable stationary solutions with periodic profile. In this context, it is natural to ask about the fate of trajectories composed of interfaces between steady configurations with periodic pattern and in particular, to study their propagation as traveling fronts. Here, we investigate such fronts in piecewise affine bistable recursions on the one-dimensional lattice. By introducing a definition inspired by symbolic dynamics, we prove the existence of front solutions and uniqueness of their velocity, upon the existence of their ground patterns. Moreover, the velocity dependence on parameters and the co-existence of several fronts with distinct ground patterns are also described. Finally, robustness of the results to small \(C^1\)-perturbations of the piecewise affine map is argued by mean continuation arguments.


Periodic fronts Bistable recursions Space–time discrete systems Symbolic dynamics. 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Grupo de Física MatemáticaUniversidade de LisboaLisbonPortugal
  2. 2.Departamento de MatemáticaInstituto Superior Técnico. Universidade Técnica de LisboaLisbonPortugal
  3. 3.Centre de Physique Théorique, UMR 7332CNRS, Aix-Marseille Université, Université de ToulonMarseille CEDEX 9France

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