What are complex systems?
(Thanks to Troy Shinbrot for contributing to this answer) Complex systems are spatially and/or temporally extended nonlinear systems characterized by collective properties associated with the system as a whole–and that are different from the characteristic behaviors of the constituent parts. While, chaos is the study of how simple systems can generate complicated behavior, complexity is the study of how complicated systems can generate simple behavior. An example of complexity is the synchronization of biological systems ranging from fireflies to neurons (e.g. Matthews, PC, Mirollo, RE & Strogatz, SH “Dynamics of a large system of coupled nonlinear oscillators,” Physica 52D (1991) 293-331). In these problems, many individual systems conspire to produce a single collective rhythm. The notion of complex systems has received lots of popular press, but it is not really clear as of yet if there is a “theory” about a “concept”. We are withholding judgment. See • http://www.calresco.org/inde
The most famous quote about Complex Systems comes from Aristole who said that “The whole is more than the sum of its parts”. Complex systems are systems where the collective behavior of their parts entails emergence of properties that can hardly, if not at all, be infered from properties of the parts. Examples of complex systems include ant-hills, ants themselves, human economies, climate, nervous systems, cells and living things, including human beings, as well as modern energy or telecommunication infrastructures.
