PACS 05.45.-a – Nonlinear dynamics and chaos PACS 47.54.-r – Pattern selection; pattern formation

Abstract – We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto a cylindrical phase space. Starting from a normal form that describes the nonequilibrium Ising-Bloch bifurcation in the continuum and using symmetry arguments, we derive a simple dynamical system that captures the dynamics of fronts in the lattice. We can expect our approach to be extended to other pattern-forming problems on lattices. Copyright c © EPLA, 2008 Extended systems on lattices have played a major role in the development of nonlinear science. One may recall celebrated models as the discrete sine-Gordon equation or the Fermi-Pasta-Ulam experiment. Usually, the develop-ment of the field has been associated with conservative systems, but dissipative lattices have attracted growing attention in the last two decades (see [1] for a review)