Kinks Dynamics in One-Dimensional Coupled Map Lattices

Details Kinks Dynamics in One-Dimensional Coupled Map Lattices Kinks Dynamics in One-Dimensional Coupled Map Lattices

1994-10-20

arxiv.org/abs/chao-dyn/9410004v1

Nonlinear Sciences

Chaotic Dynamics

17pages, LaTex,3 fig available on cpt.univ-mrs.fr directory pub/preprints/94/dynamical-systems/94-P.3079

Scientific paper

10.1063/1.166129

We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied : the non-propagating and the propagating one. In the first case, after proving the existence of such solutions, we show how they can be described using Taylor expansions. The second situation deals with the assumption of a travelling wave to follow the kink propagation. Then a comparison with the corresponding continuous model is proposed. We find that these methods are useful in simple dynamical situations but their application to complex dynamical behaviour is not yet understood.

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