Toward a theory of cellular systems

The theory of linear systems is a black box concept where the boxes are described by means of transfer functions. By use of the state-space concept the system theoretical approach is applicable to nonlinear input-output systems, too. Neural networks, which are highly structured systems, are built up of interconnected identical nonlinear components of a very simple type. The availability of VLSI technology has had a great impact on the development of these electronic cellular structures. The classical theory of time systems is not well-adapted for analysing such `cellular systems´ varying in space and time. The authors present a conception of space-time systems developed by Wunsch (1975, 1977), and show that this concept is very suitable for a system-theoretical description of the class of cellular neural networks discovered by L.O. Chua and L. Yang (1988)