Realizability and general dynamical systems

Abstract The realizability problem in the dynamical systems theory is concerned with the existence of a family of state transition functions for a given response function (e.g., weighting pattern for the case of linear systems) meaning that the latter can be realized by a dynamical system. The results giving realizability conditions are well known for the continuous differential equations systems [see, e.g., 1, 2]. The objective of this paper is to present a general realization theory which will cover not only nonlinear systems but also those systems that are not necessarily continuous or even defined on the topological spaces. Actually, the results reported represent yet another step in the development of a mathematical theory of general systems following a program outlined earlier [3–5 ]. Consistent with that program the concept of a general dynamical system is introduced using minimal mathematical structure and the realizability theory is developed as such on a general level.