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# A review of common characteristics of complex systems

Complex systems as defined here can be found in very different places, for example in nature, traffic, our brains, the economy and society. Complexity science deals with the common characteristics of complex systems and also tries to understand the differences between complex systems in different fields.

Here we can only touch upon the most important common characteristics of complex systems that have been found so far. Later in this course some of them will be elaborated upon.

## Emergence

Complex systems show emergent behaviour. Out of the interactions between the individual elements in the systems emerges behaviour at the level of the system as a whole. This so-called higher order behaviour cannot simply be derived by aggregating behaviour at the level of the elements. The whole is more than the sum of its parts. This higher order was not intended by the elements. It is a spontaneous order.

## Sudden transitions/ tipping-points/ non-linearity

Complex systems show non-linear dynamics. That means that they may suddenly change behaviour or move to another regime. They may move from a high degree of stability to very unstable behaviour. Think for example about revolutions and financial crises. A very moving description and literary account of the rather sudden cultural breakdown in Austro-Hungarian society at the beginning of the 20th century can be found in the book The World of Yesterday by the author Stefan Zweig, finalised just before he committed suicide in 1942.

## Limited predictability

The behaviour of complex systems cannot be predicted well. Small changes in initial conditions or history can lead to very different dynamics over time. The existence of non-linear behaviour also adds to unpredictability.

## Large events

Relatively small changes may lead to large effects. This is the case if a complex system is close to a tipping point and it is therefore related to the non-linearities of complex systems. These are the result of the inter-connectivity of complex systems. Pressure may build up over time and then erupt suddenly and forcefully. Large events do happen more frequently than expected on the basis of the normal distribution of events. Events that are almost impossible according to the normal distribution have a low probability in a complex system. They are not impossible. They are so called Black Swans. They follow a so called power-law or log linear distribution.

## Evolutionary dynamics

Complex adaptive systems often follow evolutionary dynamics. The mechanism of evolution starts with variation. Then there is selection of elements that are fit for the changed conditions. These elements flourish and multiply in the system. They may also change the external environment of the system, causing new variation. New variation may also come from outside the system. A new cycle of variation-selection-multiplication-variation starts. The system is never at rest. There is no movement to a knowable “end point” or equilibrium. There is constant change and innovation.

## Self-organisation

Complex adaptive systems operate without central control. They, as it were, organise themselves bottom-up.

## Fundamental Uncertainty

Complex adaptive systems are extremely hard to predict in great detail. This means their future is fundamentally uncertain. In the next activities of this week we will introduce the notion of uncertainty, how it differs from risk and how this relates to complexity.