By Prof. Dr. Werner Krabs, Dr. Stefan Wolfgang Pickl (auth.), M. Beckmann, H. P. Künzi, Prof. Dr. G. Fandel, Prof. Dr. W. Trockel, C. D. Aliprantis, A. Basile, A. Drexl, G. Feichtinger, W. Güth, K. Inderfurth, P. Korhonen, W. Kürsten, U. Schittko, R. Selten,
J. P. los angeles Salle has constructed in  a balance concept for structures of distinction equations (see additionally ) which we introduce within the first bankruptcy in the framework of metric areas. the steadiness conception for such platforms can be present in  in a marginally changed shape. we commence with self sustaining platforms within the first part of bankruptcy 1. After theoretical arrangements we learn the localization of restrict units through Lyapunov services. using those Lyapunov features we will improve a balance conception for self sustaining platforms. If we linearize a non-linear approach at a hard and fast element we can boost a balance conception for fastened issues which uses the Frechet by-product on the mounted aspect. the following subsection bargains with basic linear structures for which we intro duce a brand new proposal of balance and asymptotic balance that we undertake from . purposes to varied fields illustrate those effects. we commence with the classical predator-prey-model as being built and investigated by means of Volterra that is in accordance with a 2 x 2-system of first order differential equations for the densities of the prey and predator inhabitants, respectively. This version has additionally been investigated in  with admire to balance of its equilibrium through a Lyapunov functionality. the following we contemplate the discrete model of the model.