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A complex system is a damped, driven system (for example, a harmonic oscillator) whose total energy exceeds the threshold for it to perform according to classical mechanics but does not reach the threshold for the system to exhibit properties according to chaos theory.
Although it is arguable that humans have been studying complex systems for thousands of years, the modern scientific study of complex systems is relatively young in comparison to conventional fields of science with simple system assumptions, such as physics and chemistry. The history of the scientific study of these systems follows several different research trends.
In the area of mathematics, arguably the largest contribution to the study of complex systems was the discovery of chaos in deterministic systems, a feature of certain dynamical systems that is strongly related to nonlinearity.[1] The study of neural networks was also integral in advancing the mathematics needed to study complex systems.
The notion of nonequilibrium thermodynamics, including that pioneered by chemist and Nobel laureate Ilya Prigogine in his study of dissipative structures.
For a dynamical system to be classified as chaotic, it must have the following properties:[2]
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior.
Complex adaptive systems (CAS) are special cases of complex systems. They are complex in that they are diverse and made up of multiple interconnected elements and adaptive in that they have the capacity to change and learn from experience. 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 endeavor in a cultural and social system such as political parties or communities. This includes some large-scale online systems, such as collaborative tagging or social bookmarking systems.
The behavior of nonlinear systems is not subject to the principle of superposition while that of linear systems is subject to superposition. Thus, a complex nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts (or of their multiples).
Complex systems may have the following features:
Mathematics, Physics, Meteorology, Biology, Economics
Science, Cybernetics, Control theory, Systems biology, Systems engineering
Sociology, Internet, Family, Village, Town
Venus, Earth, Neptune, Jupiter, Mars
Computer science, Cybernetics, Psychology, Systems science, Chaos theory
Psychology, Systems science, Chaos theory, Social psychology, Control theory
Research, Learning Sciences, Complex system, Research methodology, Methodological