Title: Characterizing correlations and synchronization in collective dynamics,
Abstract: Synchronization, that occurs both for non-chaotic and chaotic systems, is a
striking phenomenon with many practical implications in natural phenomena.
However, even before synchronization, strong correlations occur in the
collective dynamics of complex systems. To characterize their nature is
essential for the understanding of phenomena in physical and social sciences.
The emergence of strong correlations before synchronization is illustrated in a
few piecewise linear models. They are shown to be associated to the behavior of
ergodic parameters which may be exactly computed in some models. The models are
also used as a testing ground to find general methods to characterize and
parametrize the correlated nature of collective dynamics.