Complex Adaptive System

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A Complex Adaptive System (CAS) is a special case of a complex system which is also adaptive, i.e. it has the ability to change and adapt itself to the environment. Typically it consists of a large number of interacting adaptive agents. CASs are used to understand events, objects, and processes in their relationship with each other. They are 'complex' - they are diverse and made up of multiple interconnected elements - and 'adaptive' - they have the capacity to change and learn from experience. They are systems where a lot of individual adaptive agents interact and communicate with each other: complex MAS with adaptive agents. The agents of a CAS learn and change as they interact with each other. The name complex adaptive systems has been coined at the interdisciplinary Santa Fe Institute (SFI), by John H. Holland, Murray Gell-Mann and others. John H. Holland is one of the inventors of evolutionary computation and genetic algorithms, Nobel Prize laureate Murray Gell-Mann discovered quarks.



CAS are an attempt to find a new, unified way of thinking about nature, human social behavior, life and the universe itself. In general the term Complex Adaptive System (CAS) is simply used for every system and society that consists of a large number of mutually interacting agents. A CAS is a complex, often self-similar collectivity of interacting adaptive agents. The study of CAS focus on the emergent, self-organizing and macroscopic properties of these complex systems. Various definitions have been offered by different researchers:

  • John H. Holland
A Complex Adaptive System (CAS) is a dynamic network of many agents (which may represent cells, species, individuals, firms, nations) acting in parallel, constantly acting and reacting to what the other agents are doing. The control of a CAS tends to be highly dispersed and decentralized. If there is to be any coherent behavior in the system, it has to arise from competition and cooperation among the agents themselves. The overall behavior of the system is the result of a huge number of decisions made every moment by many individual agents. (Source: M. Waldrop's book about "Complexity: The Emerging Science at the Edge of Order and Chaos"). According to John Holland, a complex adaptive system "can function (or continue to exist) only if it makes a continued adaptation to an environment that exhibits perpetual novelty" (see his article Complex Adaptive Systems: A Primer. It interacts with the environment in a game-like way to explore the environment. It occupies or exploits a niche in the environment. And there is a tradeoff between exploration and exploitation.
  • Kevin Dooley
A CAS behaves/evolves according to three key principles: order is emergent as opposed to predetermined (c.f. Neural Networks), the system's history is irreversible, and the system's future is often unpredictable. The basic building blocks of the CAS are agents. Agents scan their environment and develop schema representing interpretive and action rules. These schema are subject to change and evolution. (Source: K. Dooley, AZ State University)
  • Murray Gell-Mann
A complex adaptive system acquires information about its environment and its own interaction with that environment, identifying regularities in that information, condensing those regularities into a kind of "schema", or model, and acting in the real world on the basis of that schema. (Source: his book "The Quark and the Jaguar: Adventures in the Simple and the Complex", p.17)
  • Stephanie Forrest
Complex adaptive systems (CAS) consist of many interacting and adapting components operating within an environment. Agents act on and are influenced by their local environment. There is no global control over the system. All agents are only able to influence other agents locally. Each agent is driven by simple mechanisms, typically condition-action rules, where the conditions are sensitive to the local environment. (Source: Forrest, 1990)
  • Other definitions
Macroscopic collections of simple (and typically nonlinearly) interacting units that are endowed with the ability to evolve and adapt to a changing environment. (Source [1])

It is not surprising that there is no formal definition, because the term starts with "COMPLEX". Like the related concepts and buzzwords as complexity, self-organization and emergence, it is hard to define in a formal way. Like many other buzzwords, it loses much of its fascination and appeal if you succeed in doing it despite all difficulties.


CAS can be found in cogntitive psychology, artificial intelligence, scociology, ecology, biology, economics, and genetics. Examples of CAS with the corresponding agents in parentheses are:

  • markets (traders)
  • ecomomies (companies)
  • ecosystems (organisms)
  • immune systems (antibodies)
  • biological cells (proteins)
  • social systems (persons)
  • political systems (parties)

Another example is the stock market in which adaptive agents (traders) learn day-by-day and change their actions as they go. A good example is the immune system. It starts off simple but learns how to prevent you from getting complex illnesses. Other examples of complex adaptive systems include the social insect and ant colonies, the biosphere and the ecosystem, the brain, the cell and the developing embryo, manufacturing businesses and any social human group-based endeavour in a cultural and social system such as political parties or communities and social networks. There are close connections between the field of CAS and ALife. In both areas the principles emergence and self-organization are very important.

The terms complex adaptive systems, complexity science or the sciences of complexity are often used to describe the loose academic field that has grown up around the study of complex adaptive systems. Complexity science is like systems theory not a single theory - it encompasses more than one theoretical framework and is highly interdisciplinary, seeking the answers to some fundamental questions about living, adaptable, changeable systems.


As Robert Eisenstein, the former president of the SFI said in the SFI Bulletin from Winter 2004 Vol. 19 No. 1, "despite differences in substrate, there are common principles and mechanisms that underlie the processes by which nature organizes complex systems and how they behave. In other words, there is often simplicity within complexity." These common principles are for example universal scaling laws, similar underlying small-world or scale-free networks in complex networks, or similar forms of emergence, co-evolution and self-organization.

Simon A. Levin (2002) mentions diversity, localization and autonomy as the essential properties of a CAS:

  1. diversity and individuality of components,
  2. localized interactions among those components, and
  3. an autonomous process that uses the outcomes of those interactions to select a subset of those components for replication or enhancement.

According to Stephanie Forrest (1994), the term CAS refers to a system with the following properties:

  • Multi-Agent System A collection of primitive components, called "agents"
  • INTERACTION Interactions among agents and between agents and their environments
  • Emergence Unanticipated global properties often result from the interactions
  • Adaptation Agents adapt their behavior to other agents and environmental constraints
  • Evolution As a consequence, system behavior evolves over time

The essential property that distinguihes a complex adaptive system from a merely complex one is certainly adaptation. Adaptive means agents or populations of agents are able to learn. Either individual agents learn or the population learns, i.e. the population is subject to a process of mutation and competitive selection. In any case, learning agents are able to modify their rules according to their previous success in reacting to the environment. The more successful rules are selected, whereas the less successful rules are deleted.

Principles and Theorems

A set of basic principles is well known. Yet a theory, a set of theorems or "calculus" for these systems would be desirable. John H. Miller and Scott E. Page write in their book "Complex Adaptive Systems": "We hope that there is a complex systems equivalent of Newton's Laws of Motion". Is there any?

Cellular Automata and Agent-Based Systems are commonly used to model and simulate CAS. Is there any calculus for their complex combination of iteration and interaction? Or are they computationally irreducible, which means it is impossible in principle to shortcut or predict their behavior?


What distinguishes a CAS from a pure MAS - the counterpart from computer science to a CAS - is the focus on top-level properties and macroscopic features like self-similarity, complexity, emergence and self-organization. A multi-agent system (MAS) is simply defined as a system composed of multiple, interacting agents. In CASs, the agents as well as the system are adaptive: the system is self-similar. A CAS is a complex, self-similar collectivity of interacting adaptive agents. So there is not much difference between a CAS and a MAS in general, especially if the multi-agent system (MAS) is adaptive or subject to evolution.

Other important properties are adaptation (sometimes also named homeostasis), communication, cooperation, specialization, spatial and temporal organization, and of course reproduction. They can be found on all levels: cells specialize, adapt and reproduce themselves just like larger organisms do. Communication, cooperation takes place on all levels, from the agent to the system level.

Researchers and scientists


CAS in general (John H. Holland)

Ecosystems and Biospheres (Simon A. Levin, Timothy M. Lenton)

Immune Systems and biological systems (Stephanie Forrest)

  • Stephanie Forrest, "Emergent Computation: Self-organizing, collective, and cooperative phenomena in natural and artificial computing networks", Physica D 42 (1990) 1-11


  • John H. Miller & Scott E. Page, Complex Adaptive Systems: An Introduction to Computational Models of Social Life, Princeton University Press, 2007
  • M. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, Simon & Schuster, 1992
  • John Holland, Hidden Order: How Adaptation Builds Complexity, Basic Books, 1996
  • John H. Holland, Emergence: From Chaos To Order, Basic Books, 1999

more can be found in this list

External links

  • CAS Group at Iowa State University
  • CAS Research Site by Mark Voss
  • Santa Fe Institute - The Santa Fe Institute is devoted to creating a new kind of scientific research community, one emphasizing multidisciplinary collaboration in pursuit of understanding the common themes that arise in natural, artificial, and social systems. This unique scientific enterprise attempts to uncover the mechanisms that underlie the deep simplicity present in our complex world.
  • A description of complex adaptive systems on the Principia Cybernetica Web (a project that aims to develop a complete philosophy or worldview, based on the principles of evolutionary cybernetics, and supported by collaborative computer technologies)
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