Control and selection of spatiotemporal patterns in dissipative systems: Two approaches
Two different pattern forming systems are discussed by means of two
In the first part of the talk, the influence of prestructured substrates on the process of pattern formation in Langmuir-Blodgett transfer experiments is studied using a generalized Cahn-Hilliard model. We find that the occurring synchronization effects enable a control mechanism via properties of the prestructure and facilitate the production of patterns with a broader range of features. Among other things, the production of a variety of complex patterns can be achieved through the competition of intrinsic properties of the pattern forming system and the external forcing introduced by a prestructure.
In the second part, stability properties of a single breathing localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback are investigated. The presence of the time-delayed feedback enables a direct control of the amplitude and frequency of oscillations. In particular, the variation in the delay time and the feedback strength can also lead to stabilization of the breathing solution. We also provide a bifurcation analysis of the delayed system and derive an order parameter equation, explicitly describing the temporal evolution of the localized structure in the vicinity of the bifurcation point.