Tools to Characterize the Correlated Nature of Collective Dynamics

Abstract

Synchronization, which occurs for both chaotic and nonchaotic systems, is a striking phenomenon with many practical implications for natural phenomena and technological applications. However, even before synchronization, strong correlations and complex patterns occur in the collective dynamics of natural systems. To characterize their nature is essential for understanding many phenomena in physical and social sciences as well as the perspectives to control their behavior. Because simple correlation measures are unable to characterize these collective patterns, we have developed more general methods for their detection and parametrization. The emergence of patterns of strong correlations before synchronization is illustrated in a few models. They are shown to be associated with the behavior of ergodic parameters. The models are then used as a testing ground of the new pattern characterization tools.