Discrete variational method characteristics

We have seen that delayed feedback can be an efficient method for manipulation of essential characteristics of chaotic or noise-induced spatiotem-poral dynamics in a spatially discrete front system and in a continuous reaction-diffusion system. By variation of the time delay one can stabilize particular unstable periodic orbits associated with space-time patterns, or deliberately change the timescale of oscillatory patterns, and thus adjust and stabilize the frequency of the electronic device. Moreover, with a proper choice of feedback parameters one can also effectively control the coherence of spatio-temporal dynamics, e. g. enhance or destroy it. Increase of coherence is possible up to a reasonably large intensity of noise. However, as the level of noise grows, the efficiency of the control upon the temporal coherence decreases. 

Similar formulae in terms of the Fresnel reflectances may be built up for the situation with a small number of discrete layers. A larger number of layers demands the use of a more general method in which the surface is considered in terms of a series of layers of slightly diflerent characteristics. The models that are used in practice consider the density variation to be a smooth function of the distance from the surface but also may include specifically a diflerent surface layer to account for surface roughness and the possibility of molecular segregation at the surface. 

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