Travelling fronts in an array of coupled symmetric bistable units

Details Travelling fronts in an array of coupled symmetric bistable units Travelling fronts in an array of coupled symmetric bistable units

2002-05-02

arxiv.org/abs/nlin/0205005v1

Nonlinear Sciences

Pattern Formation and Solitons

25 pages (17 figures included), submitted to Physica D

Scientific paper

10.1063/1.1586511

A symmetry breaking mechanism is shown to occur in an array composed of symmetric bistable Lorenz units coupled through a nearest neighbour scheme. When the coupling is increased, we observe the route: standing --> oscillating --> travelling front. In some circumstances, this route can be described in terms of a gluing of two cycles on the plane. In this case, the asymptotic behaviour of the velocity of the front is found straightforward. However, it may also happen that the gluing bifurcation involves a saddle-focus fixed point. If so, front dynamics may become quite complex displaying several oscillating and propagating regimes, including chaotic (Shil'nikov-type) front propagation. Finally, we compare our results with different couplings and with other discrete bistable media.

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