Complex adaptive systems are special cases of complex systems, often defined as a 'complex macroscopic collection' of relatively 'similar and partially connected micro-structures' – formed in order to adapt to the changing environment, and increase its survivability as a macro-structure.
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.
The fields of CAS and artificial life are closely related. 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.
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."
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 defined as a system composed of multiple interacting agents; where as in CAS, the agents as well as the system are adaptive and 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 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, in some cases, can be analysed with game theory.
Some of the most important characteristics of complex systems 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. Moreover, the elements interact dynamically, and the interactions can be physical or involve the exchange of information
Such interactions are rich, i.e. any element or sub-system in the system is affected by and affects several other elements or sub-systems
The interactions are non-linear: small changes in inputs, physical interactions or stimuli can cause large effects or very significant changes in outputs
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 may be 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
Complex systems have a history. They evolve and their past is co-responsible for their present behaviour
Elements in the system may be ignorant of the behaviour of the system as a whole, responding only to the information or physical stimuli available to them locally
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
CAS are occasionally modeled by means of agent-based models and complex network-based models. Agent-based models are developed by means of various methods and tools primarily by means of first identifying the different agents inside the model. Another method of developing models for CAS involves developing complex network models by means of using interaction data of various CAS components.
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. This observation has led to the common misconception of evolution being progressive and leading towards what are viewed as "higher organisms".
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. Indeed, some artificial life simulations have suggested that the generation of CAS is an inescapable feature of evolution.
However, the idea of a general trend towards complexity in evolution can also be explained through a passive process. 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 microscopicprokaryotes, which comprise about half the world's biomass and constitute the vast majority of Earth's biodiversity. 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.
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