Structure of Complex Systems

Complexity may arise from complicated (nonlinear) relations, but in this context it is primarily meant to express unexpected behaviour due to the interaction of a large number of simpler subsystems. This interaction may be ‘physical’ (in the broadest sense of the word; e.g., genome-scale physo-chemical models of living cells), or of a communication and computation type. Examples of man-made complex systems often entail a ‘physical layer’ and a ‘communication, computation, and control’ layer (sometimes called a ‘cyber’-layer), which are tightly connected so that their coupling further contributes to the complexity.

For example, in smart power grids the physical layer is the power network together with its physical components (generators, lines, loads, etc.), while the cyber-layer comprises the sensors, the local and distributed controllers, as well as the overall communication and computation infra-structure. The interaction between system components of complex systems is often formalized by networks, or layers (or even networks) of networks. The network structure can be relatively fixed, but also may evolve in time, depending on internal or external inputs or events. A typical example of an evolving (man-made) network is the world-wide web. In this connection it is relevant to mention Systems-of-Systems: a set of interacting or interdependent systems connected to satisfy a global purpose having as defining characteristics: operational independence, managerial independence, geographical distribution, evolutionary development, and emergent behaviour.