Eur. Phys. J. D 59, 43-51 (2010)
https://doi.org/10.1140/epjd/e2010-00084-9

Control and managing of localized states in two-dimensional systems with periodic forcing

¹ Departamento de Física, FCFM, Universidad de Chile, Casilla 487-3, Santiago, Chile
² INLN, Université de Nice Sophia-Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne, France
³ Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile

Corresponding author: ^a marcel@dfi.uchile.cl

Received: 10 December 2009
Revised: 6 February 2010
Published online: 30 March 2010

Abstract

We study the formation of localized structures in two-dimensional systems with periodic forcing, showing that these types of systems provide an adequate framework for the study and control of localized structures. Theoretically, we introduce a dissipative ϕ⁴ model as a prototype for a bistable spatially forced system, and we show that with different spatial forcings of small amplitudes, such as square or hexagonal grids, this model exhibits a family of localized structures. By changing the forcing parameters, we control the bistability between the various induced patterns. Experimentally, based on an optical feedback with spatially amplitude-modulated beam, we set-up a two-dimensional forced experiment in a nematic liquid crystal cell. By changing the forcing parameters, the system exhibits a family of localized structures that are confirmed by numerical simulations for the average liquid crystal tilt angle.