Traveling fronts in an array of coupled symmetric bistable units.

Abstract

Traveling fronts are shown to occur in an array of nearest-neighbor coupled symmetric bistable units. When the local dynamics is given by the Lorenz equations we observe the route: standing-->oscillating-->traveling front, as the coupling is increased. A key step in this route is a gluing bifurcation of two cycles in cylindrical coordinates. When this is mediated by a saddle with real leading eigenvalues, the asymptotic behavior of the front velocity is found straightforwardly. If the saddle is focus-type instead, the front's dynamics may become quite complex, displaying several oscillating and propagating regimes and including (Shil'nikov-type) chaotic front propagation. These results stand as well for other nearest-neighbor coupling schemes and local dynamics.