Variability and reliability in high-dimensional chaotic systems (VACOSCAD)
The project plans to develop a long-term research
program to consolidate our lines of research in variability and
reliability in chaotic systems. In particular, the present proposal aims
to become one step closer to applications, by considering not only
spatially extended systems, but also models with a networked structure,
where some kind of scaling is also to be expected. We point not only to
more complicated geometries, but also to systems with more than one
characteristic scale, like the atmosphere-ocean system, neuronal
networks, and other complex systems.
We focus here on two related
aspects: variability and reliability. One of our goals is to achieve a
complete theory for the variability of the Lyapunov growth in
high-dimensional systems, since this is related with the fluctuations of
the predictability horizon (and other more fundamental problems).
networked systems with chaos at a macroscopic level are part of our
proposal. In neural systems, collective chaos– developing in a
time-scale different from the microscopic dynamics of the spiking
neurons– is usually observed. The relationship with the reliable (i.e.,
consistent and robust) 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– a process usually termed 'data
assimilation'. We plan to improve the assimilation algorithm known as
'nudging'. This is intimately related with synchronization of
spatio-temporal chaos, which is connected with surface roughening
enabling us to foresee a significant progress.