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System whose behavior is not automatically predictable from its parts

A complex adaptive system is a system that is complex in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. It is adaptive in that the individual and collective behavior mutate and self organize corresponding to the change initiating micro event or collection of events. It is a "complex macroscopic collection" of relatively "similar and partially connected micro structures" formed in order to adapt to the changing environment and increase their survivability as a macro structure. The study of complex adaptive systems, a subset of nonlinear dynamical systems, is an interdisciplinary matter that attempts to blend insights from the natural and social sciences to develop system level models and insights that allow for heterogeneous agents, phase transition, and emergent behavior.

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 interdisciplinary, seeking the answers to some fundamental questions about living, adaptable, changeable systems. Complex adaptive systems may adopt hard or softer approaches. Hard theories use formal language that is precise, tend to see agents as having tangible properties, and usually see objects in a behavioral system that can be manipulated in some way. Softer theories use natural language and narratives that may be imprecise, and agents are subjects having both tangible and intangible properties. Examples of hard complexity theories include Complex Adaptive Systems (CAS) and Viability Theory, and a class of softer theory is Viable System Theory. Many of the propositional consideration made in hard theory are also of relevance to softer theory. From here on, interest will now center on CAS. The study of CAS focuses on complex, emergent and macroscopic properties of the system. Typical examples of complex adaptive systems include: climate; cities; firms; markets; governments; industries; ecosystems; social networks; power grids; animal swarms; traffic flows; social insect (e. g. ant) colonies; The internet and cyberspace—composed, collaborated, and managed by a complex mix of human–computer interactions, is also regarded as a complex adaptive system. The term complex adaptive system was coined in 1968 by sociologist Walter F. Buckley who proposed a model of cultural evolution which regards psychological and socio cultural systems as analogous with biological species. In the modern context, complex adaptive system is sometimes linked to memetics, or proposed as a reformulation of memetics. Michael D. Cohen and Robert Axelrod however argue the approach is not social Darwinism or sociobiology because, even though the concepts of variation, interaction and selection can be applied to modelling 'populations of business strategies', for example, the detailed evolutionary mechanisms are often distinctly unbiological. As such, complex adaptive system is more similar to Richard Dawkins's idea of replicators.

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; whereas 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 characterized 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 analyzed with game theory.

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. 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. If there is a lack of an overall trend towards complexity in biology, this would not preclude the existence of forces driving systems towards complexity in a subset of cases. These minor trends would be balanced by other evolutionary pressures that drive systems towards less complex states.