Multiscale Chaotic Systems: Variability, Predictability, and Assimilation (MultiChaoS)
This project aims to study dynamical systems that are not only high-dimensional and chaotic, but alsocharacterized by more than one spatio-temporal scale. This is the case of the atmosphere-ocean system, neuronal networks, electromagnetic plasmas, and many other complex systems. We focus here on three related aspects: variability, predictability, and assimilation.
One of our goals is to achieve a complete theory for the variability of the Lyapunov growth, since this is related with the fluctuations of the predictability horizon (and other more fundamental problems). Also, networked systems with chaos at a macroscopic level are part of our proposal. In neural systems, macroscopic chaos– developing in a time-scale different from the microscopic dynamics of the spiking neurons– is usually observed. The relationship with the reliable neural processing of information is one the ultimate aims of our research.
Finally, and common to any problem related with predictability and forecasting, we plan to deal with the problem of incorporating into our model the best estimation of the state of the system under study, in a process called 'assimilation'. We plan to improve the assimilation algorithm known as 'nudging', which is intimately related with synchronization of spatio-