The dynamic behaviour of boolean systems comprising feedback loops

Abstract

In the absence of non-linear interactions, systems comprising feedback loops display the same type of “trivial” behaviour as systems without loops ; they tend towards a single stable steady state. If one or more interaction is sufficiently non-linear, looped systems can display a “non trivial” behaviour such as multiple steady states or sustained oscillations (see Nicolis and Prigogine, 1978 ; Othmer, 1976 ; for a more detailed bibliography, see chapter XIV by Richelle). Non trivial behaviours can also be found if the system combines a mild non linearity with appropriate time delays (see Richelle, 1977 ; this book, chapter XIV).