Complex system

From Academic Kids

A complex system is a system whose properties are not fully explained by an understanding of its component parts. Complex systems consist of a large number of mutually interacting and interwoven parts, entities or agents. They are woven out of many parts, the Latin complexus comes from the Greek pleko or plektos, meaning "to plait or twine." (Gell-Mann). Complex systems is also often used as a broad term addressing a research approach which includes ideas and techniques from chaos theory, artificial life, evolutionary computation and genetic algorithms.



Various definitions of complex systems have been used. A special edition of Science about complex systems Science Vol. 284. No. 5411 (1999) ( highlighted several:

  • A complex system is a highly structured system, which shows structure with variations (Goldenfeld and Kadanoff)
  • A complex system is one whose evolution is very sensitive to initial conditions or to small perturbations, one in which the number of independent interacting components is large, or one in which there are multiple pathways by which the system can evolve (Whitesides and Ismagilov)
  • A complex system is one that by design or function or both is difficult to understand and verify (Weng, Bhalla and Iyengar)
  • A complex system is one in which there are multiple interactions between many different components (D. Rind)
  • Complex systems are systems in process that constantly evolve and unfold over time (W. Brian Arthur).

Complex systems are the essential elements of science and technology. Science is all about exploration of complex systems, engineering about exploitation of complex systems. In science we would like to understand complex systems (discover simple rules and equations which lead to complex phenomena), in technology and engineering we would like to master them (create a simple user interface for complex devices and conceal complex tools and instruments behind simple interfaces).

Since they are difficult to understand, a central problem in science and engineering is the ability to predict and control the behavior of these systems. Responsible for the difficulties in understanding complex systems are a number of phenomena and mechanisms, some of which are listed below. It is also often used as a broad term addressing a research approach which includes ideas and techniques from chaos theory, artificial life, evolutionary computation and genetic algorithms. Systems thinking is another approach which attempts to study systems in a holistic way, to take account of the kinds of complexity found in complex systems.

Features of complex systems

Emergence - more is different

What distinguishes a complex system from a merely complicated one is that some behaviors and patterns emerge in complex systems as a result of the patterns of relationship between the elements. Emergence is perhaps the key property of complex systems and a lot of work is being done to try to understand more about its nature and the conditions which will help it to occur.

The behavior of a complex sytem can not be understood in terms of a simple extrapolation of the properties of its components, elements and entities. As P.W. Anderson said in his 1972 science article (Science Vol. 177 No. 4047), more is different. At the macroscopic level of the system, new properties appear which can not be predicted by the properties of microscopic components.

Typically, the relationships between elements in a complex system are both short-range and long-range. The direct local interactions are short-range, that is information is normally received from near neighbours. Through top-down feedback and small-world connections agents can indirect influence all other agents. The richness of the connections means that communications will pass across the system but will probably be modified on the way.

Relationships are non-linear

There are rarely simple cause and effect relationships between elements. A small stimulus may cause a large effect (see butterfly effect), or no effect at all. See nonlinearity.

Relationships contain feedback loops

Both negative (damping) and positive (amplifying) feedback are key ingredients of complex systems. The effects of an agent's actions are fed back to the agent and this, in turn, affects the way the agent behaves in the future. This set of constantly adapting nonlinear relationships lies at the heart of what makes a complex system special.

Complex systems are open

Complex systems are open systems - that is, energy and information are constantly being imported and exported across system boundaries. Because of this, complex systems are usually far from equilibrium: even though there is constant change there is also the appearance of stability.

The parts cannot contain the whole

There is a sense in which elements in a complex system cannot "know" what is happening in the system as a whole. If they could, all the complexity would have to be present in that element. Yet since the complexity is created by the relationships between elements that is simply impossible. A corollary of this is that no element in the system could hope to control the system.

Complex systems have a history

The history of a complex system is important and cannot be ignored. Even a small change in circumstances can lead to large deviations in the future. This has been referred to as the "Butterfly effect."

Complex systems are nested

Another key aspect of complex adaptive systems is that the components of the system - usually referred to as agents - are themselves complex adaptive systems. For example, an economy is made up of organisations, which are made up of people, who are systems of organs controlled by their nervous systems and endocrine systems, which are made up of cells - all of which, at each level in the hierarchy, are complex adaptive systems.

Boundaries are difficult to determine

It is usually difficult to determine the boundaries of a complex system. The decision is usually based on the observer's needs and prejudices rather than any intrinsic property of the system itself.

For instance, the boundary of an individual human being may appear easy to determine but a little more thought will show some of the ambiguities. For instance, are clothes inside or outside the boundary? If someone stares at you across a room or crowded train, especially in a lustful or aggressive way, have they invaded your boundary? Are your boundaries physical, or emotional? Emotional influence can impact physical existence. At what moment does food become a part of your body?

Complex networks

A complex network forms the backbone of complex systems: the nodes correspond to the agents, entities or parts of the complex system, the edges to the interactions between them. The most complex networks are small-world or scale-free networks at the border between regular and random networks.

Examples and tools

The world is full of complex systems, and many are vitally important: from a single cells to complete biological organisms; the climate and weather systems; ecological and economic systems; the brain or the nervous system.

Cellular automata can be used to study pattern formation in nature. Simple rules in CA can produce very complex structures and patterns. A multi-agent system can be used to study the phenomena in complex adaptive systems, which are composed of several agents, capable of mutual interaction.


  • From Sync by Steven Strogatz: "Every decade or so, a grandiose theory comes along, bearing similar aspirations and often brandishing an ominous-sounding C-name. In the 1960 it was cybernetics. In the '70s it was catastrophe theory. Then came chaos theory in the '80s and complexity theory in the '90s."


Complex Adaptive System

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