What Makes a System Complex? - An Approach to Self Organization and Emergence

Abstract

Men in their arrogance claim to understand the nature of Creation, and devise elaborate theories to describe its behaviour. But always they discover in the end that God is more clever than they thought Sister Miriam GodwinsonThe fast changing reality in technical and natural domains perceived by always more accurate observations has drawn the attention on a new and very broad class of systems mainly characterized by specific behaviour which has been entered under the common wording "complexity". Based on elementary system graph representation with components as nodes and interactions as vertices, it is shown that systems belong to only three states : simple, complicated, and complex, the main properties of which are discussed. The first two states have been studied at length over past centuries, and the last one finds its origin in the elementary fact that when system performance is pushed up, there exists a threshold above which interaction between components overtake outside interaction. At the same time, system self-organizes and filters corresponding outer action, making it more robust to outer effect, with emergence of a new behaviour which was not predictable from only components study. Examples in Physics and Biology are given, and three main classes of "complexity" behaviour are distinguished corresponding to different levels of difficulty to handle the problem of their dynamics. The great interest of using complex state properties in man-made systems is stressed and important issues are discussed. They mainly concentrate on the difficult balance to be established between the relative system isolation when becoming complex and the delegation of corresponding new capability from (outside) operator. This implies giving the system some "intelligence" in an adequate frame between the new augmented system state and supervising operator, with consequences on the canonical system triplet {effector-sensor-controller} which has to be reorganized in this new setting. Moreover, it is observed that entering complexity state opens the possibility for the function to feedback onto the structure, ie to mimic at technical level the invention of Nature over Her very long history.

Complexity of chemical products, plants, processes and control systems

“…On the other hand, the modelling of an existing complex system requires assumptions (Cotsaftis, 2007). The precipitation of a solid is simple in its concept, but complex in operation.…”

Integrating Particle Microstructure, Surface and Mechanical Characterization with Bulk Powder Processing

“…However, the type of complexity, or lack thereof, resides on the specific property in question and on the type of behavior it elicits on the powder. According to classical systems theory, systems can be Simple, Complicated or Complex (Cotsaftis M., 2009)-the uppercase notation on this first instance is meant to reflect that, as used here, these terms carry specific meanings. Accordingly, a simple system is one where each agent (particle in the case of powders) is weakly coupled with other agents.…”

Emergence and complex systems: The contribution of dynamic graph theory

“…One should avoid reducing a hierarchical system merely to the set of its components, but this seems to be common practice (Cotsaftis, 2009b). The popular statement that 'the whole is more than the sum of its parts' is just the (not very surprising) observation that relations are important.…”

“…The causal loop is considered the first step towards self-organisation (De Wolf & Holvoet, 2005). Cotsaftis (2009b) considers that a system is complex when 'self-organisation filters out external action, making the system more robust to outer effects'. In ecology, Ulanowicz (1990) builds upon this result to demonstrate that feedback loops in trophic networks disrupt the overwhelming physical linear causation to yield a different logic, where the stability of cycles arises from a constant throughput of energy or matter.…”