FAST AND SLOW FEEDBACK IN SYSTEMS THEORY

Biological systems are complex systems with feedback. Very often the scales for the dynamics of the system and the dynamics of the feedback are very different. The mathematical tool used to deal with this different time scales is Tikhonov's theorem which permits to reduce the complexity of the system through suitable approximations. This paper presents a theory of two time scales feedback systems phrased in the language of Nonstandard Analysis (NSA), introduced in the sixties by A. Robinson. Our opinion is that this presentation is more understandable for a non-mathematicaly trained reader than the classical one. Th paper is entirely self contained. A short but comprehensive tutorial on NSA is provided and precise definitions for concepts from systems theory are given.