Localized States in Bi‐Pattern Systems

Abstract

We present a unifying description of localized states observed in systems with coexistence of two spatially periodic states, called bi‐pattern systems. Localized states are pinned over an underlying lattice that is either a self‐organized pattern spontaneously generated by the system itself, or a periodic grid created by a spatial forcing. We show that localized states are generic and require only the coexistence of two spatially periodic states. Experimentally, these states have been observed in a nonlinear optical system. At the onset of the spatial bifurcation, a forced one‐dimensional amplitude equation is derived for the critical modes, which accounts for the appearance of localized states. By numerical simulations, we show that localized structures persist on two‐dimensional systems and exhibit different shapes depending on the symmetry of the supporting patterns.