• What is a complex system?
• Complex or just complicated?
• Complex Systems Science

What is a complex system?

Genomes, ecosystems, stock markets, the weather and society are all examples of complex systems – large aggregations of many smaller interacting parts. These parts may be species, investors, air particles or individuals.

Complex or just complicated?

Two properties set a complex system apart from one that is merely complicated:

• emergence
• self-organisation. 

Emergence is the appearance of behaviour that could not be anticipated from a knowledge of the parts of the system alone.

Cyclones, tornadoes or weather systems are emergent features of the motion of air particles on the spinning Earth. Financial recessions and booms are emergent features of national economies.

Complicated artefacts like motor cars or power plants also have emergent features in this sense so a further property is needed to distinguish complex systems.

This is self-organisation. This means that there is no external controller or planner engineering the appearance of these emergent features. They appear spontaneously.

Complex Systems Science

It has recently been realised that there are general laws and rules governing these processes which apply equally to the weather, to society and to life itself.

A key feature of real systems that has proved to be essential in the appearance of rich emergent features is local interaction. In other words, elements of a system only interact with their neighbours.

These interactions can be represented by simple rules that describe how the state of any element in the system is dependent on the state of its neighbours. For example, transmission of a disease usually depends on contact between individuals. Simple models of epidemics that assume a 'well-mixed' population often fail to predict the rate of spread and resistance to eradication of many diseases.

Scientists are now developing computer models of complex systems based on local interaction rules. In the social domain, the resulting computer models are reshaping our understanding of social and economic processes including phenomena like societal resilience and collapse.