Characterizing correlations and synchronization in collective dynamics

TL;DR

This paper investigates the nature of correlations and synchronization in complex systems, emphasizing the importance of understanding pre-synchronization correlations through models and ergodic parameters.

Contribution

It introduces methods to characterize and parametrize correlations in collective dynamics, highlighting their emergence prior to synchronization in piecewise linear models.

Findings

Strong correlations occur before synchronization in models.

Ergodic parameters can be exactly computed in some cases.

Models serve as testing grounds for new characterization methods.

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.