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.
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.
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