Complex systems which evolve towards homeostasis

Abstract

It is still not well understood how large complex systems (such as ecosystems) come into being or how they persist over long periods of time, although recent studies1–5 have clarified certain aspects of the associated stability problems. The occurrence of such systems presents no problem if a ideological assumption is valid—that is, if the variables may be presumed (or compelled) to adjust their mutual interactions in advance, to achieve the desired persistence. But when no such ‘foresight’ is credible, a real problem emerges; how a given variable can interact will generally be constrained by factors internal to it, independent of the ‘needs’ of other variables or of system stability. This consideration has prompted studies of ‘randomly-interacting’ system models, and interesting results have emerged1–4 concerning the stability of such models—that is, their capacity to return to equilibrium after a fluctuation. However, the question remains: how did such a collection of randomly-interacting entities arrive at an equilibrium in the first place? We present here results from a simple model using mutually interacting variables. We show how, even on assumptions which make large complex and persistent systems highly improbable initially, they can nevertheless be expected to arise in profusion in the normal course of time development.