Stabilization, Selection, and Tracking of Unstable Patterns by Weak Spatial Perturbations

Abstract

A spatial perturbation method for the stabilization of an unstable state of a pattern forming system is presented. The perturbation, as a weak driving signal, mimics the target pattern. Stabilization, selection, and tracking of unstable rolls, squares, hexagons, and honeycombs are demonstrated by numerical simulations through the example of an optical system. The application of an external spatial perturbation also results in critical slowing down and resonant phenomenon.