Chaos / Meteorology

Chaos theory is basically accomplished for low-dimensional dynamical systems. Still, high-dimensional chaos remains only partly understood. We resort to numerical simulations and more or less heuristic arguments to achieve some progress. A comprehensive theory of high-dimensional chaos will make it possible to improve the predictability of complex systems, such as the atmosphere of the climate.

Initially, I focused on the Lyapunov analysis of spatially extended system with extensive chaos. A fruitful connection between the Kardar-Parisi-Zhang equation and the Lyapunov vector allowed us to make several new results on the dynamics of perturbations. Specially, interesting are perturbations used in forecasting of geophysical flows, such as the singular vectors and bred vectors.

More recently, I have explored globally coupled maps, finding a remarkable lack of universality.

In our current project, we plan to investigate chaos in random neural networks.