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Complex adaptive systems are special cases of complex systems. They are complex in that they are dynamic networks of interactions and relationships not aggregations of static entities. They are adaptive in that their individual and collective behaviour changes as a result of experience.^{[1][Need quotation to verify]}

Overview[link]

The term complex adaptive systems, or complexity science, is often used to describe the loosely organized academic field that has grown up around the study of such systems. Complexity science is 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.

Examples of complex adaptive systems include the stock market, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the developing embryo, manufacturing businesses and any human social group-based endeavour in a cultural and social system such as political parties or communities. There are close relationships between the field of CAS and artificial life. In both areas the principles of emergence and self-organization are very important.

The ideas and models of CAS are essentially evolutionary, grounded in modern chemistry, biological views on adaptation, exaptation and evolution and simulation models in economics and social systems.

Definitions[link]

A CAS is a complex, self-similar collection of interacting adaptive agents. The study of CAS focuses on complex, emergent and macroscopic properties of the system. Various definitions have been offered by different researchers:

• John H. Holland "Cas [complex adaptive systems] are systems that have a large numbers of components, often called agents, that interact and adapt or learn."^[2]

General properties[link]

What distinguishes a CAS from a pure multi-agent system (MAS) is the focus on top-level properties and features like self-similarity, complexity, emergence and self-organization. A 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. Complex Adaptive Systems are characterised by a high degree of adaptive capacity, giving them resilience in the face of perturbation.

Other important properties are adaptation (or 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 and cooperation take place on all levels, from the agent to the system level. The forces driving co-operation between agents in such a system can, in some cases be analysed with game theory.

Characteristics[link]

Complex adaptive systems are characterized as follows^[3] and the most important are:

• The number of elements is sufficiently large that conventional descriptions (e.g. a system of differential equations) are not only impractical, but cease to assist in understanding the system, the elements also have to interact and the interaction must be dynamic. Interactions can be physical or involve the exchange of information.
• Such interactions are rich, i.e. any element in the system is affected by and affects several other systems.
• The interactions are non-linear which means that small causes can have large results.
• Interactions are primarily but not exclusively with immediate neighbours and the nature of the influence is modulated.
• Any interaction can feed back onto itself directly or after a number of intervening stages, such feedback can vary in quality. This is known as recurrency.
• Such systems are open and it may be difficult or impossible to define system boundaries
• Complex systems operate under far from equilibrium conditions, there has to be a constant flow of energy to maintain the organization of the system
• All complex systems have a history, they evolve and their past is co-responsible for their present behaviour
• Elements in the system are ignorant of the behaviour of the system as a whole, responding only to what is available to it locally

Axelrod & Cohen^[4] identify a series of key terms from a modeling perspective:

• Strategy, a conditional action pattern that indicates what to do in which circumstances
• Artifact, a material resource that has definite location and can respond to the action of agents
• Agent, a collection of properties, strategies & capabilities for interacting with artifacts & other agents
• Population, a collection of agents, or, in some situations, collections of strategies
• System, a larger collection, including one or more populations of agents and possibly also artifacts.
• Type, all the agents (or strategies) in a population that have some characteristic in common
• Variety, the diversity of types within a population or system
• Interaction pattern, the recurring regularities of contact among types within a system
• Space (physical), location in geographical space & time of agents and artifacts
• Space (conceptual), “location” in a set of categories structured so that “nearby” agents will tend to interact
• Selection, processes that lead to an increase or decrease in the frequency of various types of agent or strategies
• Success criteria or performance measures, a “score” used by an agent or designer in attributing credit in the selection of relatively successful (or unsuccessful) strategies or agents.

Modeling and Simulation[link]

Cas are occasionally modeled by means of agent-based models and complex network-based models^[5]. Agent-based models are developed by means of various methods and tools primarily by means of first identifying the different agents inside the model^[6]. Another method of developing models for cas involves developing complex network models by means of using interaction data of various cas components^[7].

Evolution of complexity[link]

Passive versus active trends in the evolution of complexity. CAS at the beginning of the processes are colored red. Changes in the number of systems are shown by the height of the bars, with each set of graphs moving up in a time series.

Living organisms are complex adaptive systems. Although complexity is hard to quantify in biology, evolution has produced some remarkably complex organisms.^[8] This observation has led to the common misconception of evolution being progressive and leading towards what are viewed as "higher organisms".^[9]

If this were generally true, evolution would possess an active trend towards complexity. As shown below, in this type of process the value of the most common amount of complexity would increase over time.^[10] Indeed, some artificial life simulations have suggested that the generation of CAS is an inescapable feature of evolution.^[11][12]

However, the idea of a general trend towards complexity in evolution can also be explained through a passive process.^[10] This involves an increase in variance but the most common value, the mode, does not change. Thus, the maximum level of complexity increases over time, but only as an indirect product of there being more organisms in total. This type of random process is also called a bounded random walk.

In this hypothesis, the apparent trend towards more complex organisms is an illusion resulting from concentrating on the small number of large, very complex organisms that inhabit the right-hand tail of the complexity distribution and ignoring simpler and much more common organisms. This passive model emphasizes that the overwhelming majority of species are microscopic prokaryotes,^[13] which comprise about half the world's biomass^[14] and constitute the vast majority of Earth's biodiversity.^[15] Therefore, simple life remains dominant on Earth, and complex life appears more diverse only because of sampling bias.

This lack of an overall trend towards complexity in biology does not preclude the existence of forces driving systems towards complexity in a subset of cases. These minor trends are balanced by other evolutionary pressures that drive systems towards less complex states.

See also[link]

• Agent-based model
• Complex Networks
• Artificial life
• Center for Complex Systems and Brain Sciences
• Cognitive Science
• Command and Control Research Program
• Complex system

Systems science portal

• Computational Economics
• Computational Sociology
• Enterprise systems engineering
• Generative sciences
• Santa Fe Institute
• Simulated reality
• Sociology and complexity science
• Swarm Development Group
• Universal Darwinism

References[link]

Literature[link]

• Ahmed E, Elgazzar AS, Hegazi AS (28 June 2005). "An overview of complex adaptive systems". Mansoura J. Math 32: 6059. arXiv:nlin/0506059. Bibcode 2005nlin......6059A. arXiv:nlin/0506059v1 [nlin.AO]. 
• Bullock S, Cliff D (2004). Complexity and Emergent Behaviour in ICT Systems. Hewlett-Packard Labs. HP-2004-187. http://www.hpl.hp.com/techreports/2004/HPL-2004-187.html. ; commissioned as a report by the UK government's Foresight Programme.
• Dooley, K., Complexity in Social Science glossary a research training project of the European Commission.
• Edwin E. Olson and Glenda H. Eoyang (2001). Facilitating Organization Change. San Francisco: Jossey-Bass. ISBN 0-7879-5330-X. 
• Gell-Mann, Murray (1994). The quark and the jaguar: adventures in the simple and the complex. San Francisco: W.H. Freeman. ISBN 0-7167-2581-9. 
• Holland, John H. (1992). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. Cambridge, Mass: MIT Press. ISBN 0-262-58111-6. 
• Holland, John H. (1999). Emergence: from chaos to order. Reading, Mass: Perseus Books. ISBN 0-7382-0142-1. 
• Kelly, Kevin (1994) (Full text available online). Out of control: the new biology of machines, social systems and the economic world. Boston: Addison-Wesley. ISBN 0-201-48340-8. http://www.kk.org/outofcontrol/contents.php. 
• Pharaoh, M.C. (online). Looking to systems theory for a reductive explanation of phenomenal experience and evolutionary foundations for higher order thought Retrieved 15 January 2008.
• Hobbs, George & Scheepers, Rens (2010),"Agility in Information Systems: Enabling Capabilities for the IT Function," Pacific Asia Journal of the Association for Information Systems: Vol. 2: Iss. 4, Article 2. Link

External links[link]

• Complexity Digest comprehensive digest of latest CAS related news and research.
• Complex Adaptive Systems Group loosely coupled group of scientists and software engineers interested in complex adaptive systems
• DNA Wales Research Group Current Research in Organisational change CAS/CES related news and free research data. Also linked to the Business Doctor & BBC documentary series
• A description of complex adaptive systems on the Principia Cybernetica Web.
• Quick reference single-page description of the 'world' of complexity and related ideas hosted by the Center for the Study of Complex Systems at the University of Michigan.
• Complex systems research network
• The Open Agent-Based Modeling Consortium
• A group of multidisciplinary researchers interested in the Modeling and Simulation of Complex Adaptive Systems

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2008)

The term adaptation arises mainly in the biological scope as a trial to study the relationship between the characteristics (anatomic structure, physiological processes or behavior) of living beings and their environments. Currently, in biology, the term adaptation has a clear and concise meaning: a biological adaptation is an anatomic structure, a physiological process or a behavior's trait of an organism that has been selected by the natural evolution in such a way that this characteristic increase the probability of reproduction of an organism.^{[citation needed]}

An adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts. Feedback loops represent a key feature of adaptive systems, allowing the response to changes; examples of adaptive systems include: natural ecosystems, individual organisms, human communities, human organizations, and human families.

Some artificial systems can be adaptive as well; for instance, robots employ control systems that utilize feedback loops to sense new conditions in their environment and adapt accordingly.

The Law of Adaptation[link]

Every adaptive system converges to a state in which all kind of stimulation ceases.^[1]

A formal definition of the Law of Adaptation is as follows:

Given a system Failed to parse (Missing texvc executable; please see math/README to configure.): S , we say that a physical event Failed to parse (Missing texvc executable; please see math/README to configure.): E

is a stimulus for the system Failed to parse (Missing texvc executable; please see math/README to configure.): S
if and only if the probability Failed to parse (Missing texvc executable; please see math/README to configure.): P(S \rightarrow S'|E)
that the system suffers a change or be perturbed (in its elements or in its processes) when the event Failed to parse (Missing texvc executable; please see math/README to configure.): E
occurs is strictly greater than the prior probability that Failed to parse (Missing texvc executable; please see math/README to configure.): S
suffers a change independently of Failed to parse (Missing texvc executable; please see math/README to configure.): E

Failed to parse (Missing texvc executable; please see math/README to configure.): P(S \rightarrow S'|E)>P(S \rightarrow S')

Let Failed to parse (Missing texvc executable; please see math/README to configure.): S

be an arbitrary system subject to changes in time Failed to parse (Missing texvc executable; please see math/README to configure.): t
and let Failed to parse (Missing texvc executable; please see math/README to configure.): E
be an arbitrary event that is a stimulus for the system Failed to parse (Missing texvc executable; please see math/README to configure.): S

we say that Failed to parse (Missing texvc executable; please see math/README to configure.): S

is an adaptive system if and only if when t tends to infinity Failed to parse (Missing texvc executable; please see math/README to configure.): (t\rightarrow \infty)
the probability that the system Failed to parse (Missing texvc executable; please see math/README to configure.): S
change its behavior Failed to parse (Missing texvc executable; please see math/README to configure.): (S\rightarrow S')
in a time step Failed to parse (Missing texvc executable; please see math/README to configure.): t_0
given the event Failed to parse (Missing texvc executable; please see math/README to configure.): E
is equal to the probability that the system change its behavior independently of the occurrence of the event Failed to parse (Missing texvc executable; please see math/README to configure.): E

. In mathematical terms:

1. - Failed to parse (Missing texvc executable; please see math/README to configure.): P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0

1. - Failed to parse (Missing texvc executable; please see math/README to configure.): \lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')

Thus, for each instant Failed to parse (Missing texvc executable; please see math/README to configure.): t

will exist a temporal interval Failed to parse (Missing texvc executable; please see math/README to configure.): h
such that:

Failed to parse (Missing texvc executable; please see math/README to configure.): P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')

Benefit of Self-Adjusting Systems[link]

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of self-adjusting systems is its “adaption to the edge of chaos” or ability to avoid chaos. Practically speaking, by heading to the edge of chaos without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications.^[2]

See also[link]

Evolutionary biology portal

• Adaptive immune system
• Artificial neural network
• Complex adaptive system
• Diffusion of innovations
• Ecosystems
• Neural adaptation

References[link]

Dave Snowden

David John Snowden (born 1 April 1954) is a Welsh lecturer, consultant and researcher in the field of knowledge management.

He has been described as an expert on tacit knowledge,^[1] and "One of the most perceptive observers of the way in which knowledge is used in organizations."^[2] In 2008, he won the Academy of Management award^[3] for an "Outstanding Practitioner-Oriented Publication in OB" for a Harvard Business Review article^[4] co-authored by Mary E. Boone.

Snowden developed the Cynefin framework, a practical application of complexity theory to management science.^[5][6] The framework helps managers determine the prevailing operative context, enabling appropriate choices and decisions.^[4] Snowden explains the choice of the term Cynefin ( /ˈkʌnɨvɪn/): [it is] a Welsh word that signifies the "multiple factors in our environment and our experience that influence us in ways we can never understand".^[4] Cynefin has no direct translation into English, but its meaning is similar to 'habitat' and is also used "as an adjective used to convey 'acquainted' or 'familiar'."^[7]

He describes his three basic rules or principles of knowledge exchange:^[2][8]

"Knowledge can only be volunteered; it can't be conscripted."

"People always know more than they can tell, and can tell more than they can write."

"People only know what they need to know when they need to know it."

Professional activities[link]

Snowden was born in Ongar, Essex, England to Welsh parents. When he was three, his parents returned to Wales and Snowden grew up in Mold, Flintshire, where he was educated at the Alun School.^[9] He earned a degree in Philosophy from the University of Lancaster, where he was a member of County College. Following University he worked for the Student Christian Movement for three years. Moving into industry he obtained a Master's degree in Business Administration at Middlesex University studying part time. Following a series of roles in various organisations, he was one of the management team who bought Data Sciences from Thorn EMI. When that organisation was acquired by IBM, he became a Director in the IBM Institute for Knowledge Management and subsequently founded their Cynefin Centre for Organisational Complexity.^[9] He is currently the Founder and Chief Scientific Officer of Cognitive Edge, a research network that focuses on the development of the theory and practice of sensemaking.^[9]

Snowden is a visiting professor at the University of Pretoria, adjunct at the Hong Kong Polytechnic University, and a visiting fellow at Warwick University, Nanyang University, the Università Cattolica and the Singapore Management College. He has also held visiting positions at the universities of Canberra and Surrey. In 2008-2009 he wrote a column, for KMWorld, called Everything is fragmented on trends in technology, social issues, the scientific use of narrative.^[10] Snowden lives in Lockeridge, Wiltshire, England and, as of 2010, is an editor-in-chief of the journal, Emergence: Complexity and Organisation and a director of funding allocation for the Engineering and Physical Sciences Research Council on the subject of emergence.^[4][9][11]

Notes[link]

Works[link]

• "The art and science of Story or ‘Are you sitting uncomfortably?’", Business Information Review December 2000 vol. 17 no. 4 215-226.
• "Complex acts of knowing: paradox and descriptive self-awareness", Journal of Knowledge Management, Vol. 6 Iss: 2, 2002. pp. 100 - 111.
• "The new dynamics of strategy: Sense-making in a complex and complicated world", IBM Systems Journal, Volume: 42 Issue:3, 2003, 462 - 483.
• with Mary E. Boone, "A Leader’s Framework for Decision Making of the circumstances they face", Harvard Business Review, November 2007.

External links[link]

• List of articles by Dave Snowden
• Vinson, Jack (31 October 2007), "Dave Snowden interviewed by Jon Husband", Knowledge Jolt, http://blog.jackvinson.com/archives/2007/10/31/dave_snowden_interviewed_by_jon_husband.html, retrieved 3 February 2010