This article is from the Nonlinear Science FAQ, by James D. Meiss firstname.lastname@example.org with numerous contributions by others.
Spatio-temporal chaos occurs when system of coupled dynamical systems
gives rise to dynamical behavior that exhibits both spatial disorder (as in
rapid decay of spatial correlations) and temporal disorder (as in nonzero
Lyapunov exponents). This is an extremely active, and rather unsettled area of
research. For an introduction see:
Cross, M. C. and P. C. Hohenberg (1993). "Pattern Formation outside of
Equilibrium." Rev. Mod. Phys. 65: 851-1112.
http://www.cmp.caltech.edu/~mcc/st_chaos.html Spatio-Temporal Chaos
An interesting application which exhibits pattern formation and spatio-
temporal chaos is to excitable media in biological or chemical systems. See
Chaos, Solitions and Fractals 5 #3&4 (1995) Nonlinear Phenomena in Excitable
Physiological System, http://www.elsevier.nl/locate/chaos
Chaos focus issue on Fibrillation