This article is from the Nonlinear Science FAQ, by James D. Meiss firstname.lastname@example.org with numerous contributions by others.
(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
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/index.htm The Complexity & Artificial Life Web Site
http://www.calresco.org/sos/sosfaq.htm The self-organized systems FAQ