My research in this topic is mostly due to other related topics like pattern formation, waves in fluids or topological defects. Also, I co-organized an international school on: "Space time chaos: characterization, control and synchronization"

Introduction

Space-time chaos is much more complicated to understand than classical temporal chaos. In fact, space-time chaos can be classified under the category of high dimensional chaos. Such dimensionality refers to the embedding dimension. If the embedding dimension is finite (as for example in attractors coming from systems of ordinary differential equations) the analysis, control and even synchronization of chaos is straightforward [T. Sauer et al. J. Stat. Phys. 65 (1991) 579] [H. Kantz & T. Schreiber "Nonlinear Time Series Analysis" (1997) Cambridge University Press] [H.D.I. Abarbanel "Analysis of Observed Chaotic data" (1996) Springer-Verlag] [Introductory chapters of: (ed.) S. Boccaletti et al. "Space-Time Chaos: Characterization, Control and Synchronization" (2001) World Scientific Publishing]. However, if the embedding dimension is infinite (as could occur either in space-time systems modeled by P.D.E. or in time delayed systems modeled by difference-differential equations or in similar systems), there does not exist a universally accepted theory of this kind of chaos. It is known that topological defects play an important role in space-time chaos. As the space-time chaos occurs in d-dimensional space plus time, the emergence of chaotic states takes place in "standard" patterns [(ed.) S. Boccaletti et al. "Space-Time Chaos: Characterization, Control and Synchronization" (2001) World Scientific Publishing].