Are interactions between different time-scales a characteristic of complexity?

Abstract

A self-organized complex natural system, such as a biological, a neural or a social system, is characterized by the fact that its dynamics is generated by a network of competitive regulations, each one acting as a 'simple system' (in the Newtonian sense) at a given level of complexity and with its own time-scale. A dialectics dependent on specific structural temporal constraints is established between them, punctuated by local fractures imposing a change of strategy. Such systems are capable of anticipation and adaptation thanks to the development of a memory. The Memory Evolutive Systems (MES) defined by Ehresmann and Vanbremeersch in a series of papers since 1986 represent a mathematical model for such systems, based on the Theory of categories. This model takes into account the above properties, and it allows to study the problem of emergence; an analysis of causality attributions shows that MES satisfy the definition given by Rosen for an 'organism'.