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Complex Systems
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Remarks on Complex Systems

(Current version of Sept. 23, 2013; replaces original version of Sept. 17, 2012)

Elementary Questions and Answers

Q: What is the purpose of this non-profit site?
A: For at least the next two years, this site will gradually be extended to offer links to complex systems knowledge; try to give hints for those wishing to learn complex systems theory; and help publicize complex systems expertise in the public and private sector.

Q: Are complicated looking arrangements of objects related or equivalent to complex systems?
A: Not necessarily. An arbitrary arrangement of static objects like, for example, a random arrangement of dots on a canvas may appear to be complicated, or complex, to the casual observer but it is lacking any interaction between the individual elements and would thus be devoid of one the basic prerequisites for calling this a complex system.

Q: Are complex systems then related to some sort of or some generalization of the historic N-body problem in astronomy or to the motion of a large number of interacting particles in statistical physics?
A: Yes indeed — at least in a certain and rather limited sense. The original N-body problem rests on Newton's law of gravitation and is thus but one very special example of a system of N interacting bodies. Systems with N → ∞ and other laws of interaction are among other fields treated in statistical physics and nonlinear thermodynamics. Depending on the law of interaction describing more complicated systems, we may need a selection of methods taken from

     »  nonlinear dynamics
     »  statistical physics (especially non-equilibrium thermodynamics, quantum statistics, self-organizing systems; etc.)
     »  chemistry
     »  engineering (for example multidimensional, often nonlinear, feedback systems in control and feedback theory; traffic control, that is the interaction of drivers, vehicles and pedestrians within traffic situations, etc.)
     »  information theory
     »  the life sciences (biology, medicine): interaction of individual organisms; interaction of species; etc.

and other fields of work for adequately describing a given system. The evolution of a complex system interacting with its environment will often be characterized by a set of nonlinear equations like, for example, the equations of a multidimensional feedback system; exhibit chaotic behaviour; occasionally show off collective behaviour including self-organization; etc.
Many systems considered to be complex may actually be described as "systems of systems". Interested readers are referred to the literature or the web pages of the Complex System Society for additional detail.
Solving the equations describing a system is usually only possible using adequate numerical algorithms (keywords: computational physics / numerics, numerical simulation, etc.).

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