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).
Also, 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.