Space environment is an ideal laboratory to study the complex systems behaviour of
the universe, which is dominated by dynamical phenomona such as waves,
instabilities and turbulence. A deep understanding of space environment turbulence,
from the interior of the Sun to the near-Earth space, is essential for improving the
monitoring of Sun-Earth connections and forecasting of space weather.
The nonlinear spatiotemporal evolution of  Alfven waves in space plasmas can be
modeled by nonlinear partial differential equations such as the derivative nonlinear
Schroedinger equation and the Kuramoto-Sivashinsky equation. The chaos theory
provides a powerful tool to probe the onset of Alfven turbulence through the
solutions of  these equations using a combination of analytical and computational
techniques. Two approaches  can be adopted to study nonlinear Alfven waves:
low-dimensional dynamical system approach and high-dimensional system
approach. The former gives information on the temporal or spatial behaviours,
whereas the latter gives information on the spatiatemporal behaviours.

Chian, A. C.-L., Borotto, F. A. and Gonzalez, W. D., Astrophys. J. 505, 993 (1998)

Chian, A. C.-L., Rempel, E. L., Macau, E. E., Rosa, R. R. and Christiansen, F.,
Physical Review E (Rapid Communications) 65, 035203-1 (2002).