# Topic:Complex systems

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## Context

This topic forms part of the systems and complexity area of study. People who are competent in the topic can apply their knowledge to describe the features of complex systems and how they are distinguishable from other forms of system such as ordered, chaotic, and stochastic systems.

## Competencies

Expected competencies after study of this topic are:

- understand the difference between deterministic and nondeterministic systems
- define the characteristics of classes of deterministic and nondeterministic systems (ordered, chaotic, complex and stochastic)
- describe the behaviours that result from the essential characteristics of complex systems

## Summary

A **complex system** is a type of system that is composed of many interconnected elements that interact with each other. They:

- are highly nonlinear (unpredictable) and self-organizing
- possess an intricate level of organization and complexity
- can adapt and evolve according to their environment

By comparison:

- Ordered systems are characterised by structured and predictable behavior, characterized by linear relationships and modeled using mathematical equations
- Chaotic systems are characterised by being highly sensitive to initial conditions, determinism and nonlinearity (unpredictability)
- Stochastic systems are characterized by randomness and lack of predictability, and are usually modeled using probability theory

Complex systems spontaneously occur in many places including ecological, biological, and social systems.

## Key concepts

The fact that complex systems are not random but also not completely ordered is of central importance ... it is a necessary condition for a complex system that it exhibit some kind of spontaneous order ... [They are] organized into a variety of levels of structure and properties that interact with the level above and below ... [exhibiting] causal regularities, and various kinds of symmetry, order and periodic behaviour.—Ladyman, Lambert & Weisner, What is a complex system?

[Complex systems] maintain a recognizable form and activities over long periods of time, even though their constituent parts exist on time scales that are orders of magnitude less long lived ... [each] consists of a set of diverse actors who dynamically interact with one another awash in a sea of feedbacks.—John H. Miller and Scott E. Page, [1]

## Primers

- Introduction to Complexity: What are Complex Systems? (Video)
- An Introduction to Complex Systems Science and its Applications

## Further reading

- Ladyman, Lambert & Weisner: What is a Complex System?
- Universal resilience patterns in complex networks