Classification and spatiotemporal correlation of dominant fluctuations in complex dynamical systems

The behaviors of many complex systems, from nanostructured materials to animal colonies, are governed by local events/rearrangements that, while involving a restricted number of interacting units, may generate collective cascade phenomena. Tracking such local events and understanding their emergence and propagation in the system is often challenging. Common strategies consist, for example, in monitoring over time parameters (descriptors) that are designed ad hoc to analyze certain systems. However, such approaches typically require prior knowledge of the system's physics and are poorly transferable. Here, we present a general, transferable, and agnostic analysis approach that can reveal precious information on the physics of a variety of complex dynamical systems starting solely from the trajectories of their constitutive units. Built on a bivariate combination of two abstract descriptors, Local Environments and Neighbors Shuffling and TimeSmooth Overlap of Atomic Position, such approach allows to (i) detect the emergence of local fluctuations in simulation or experimentally acquired trajectories of multibody dynamical systems, (ii) classify fluctuations into categories, and (iii) correlate them in space and time. We demonstrate how this method, based on the abstract concepts of local fluctuations and their spatiotemporal correlations, may reveal precious insights on the emergence and propagation of local and collective phenomena in a variety of complex systems ranging from the atomic- to the macroscopic-scale. This provides a general data-driven approach that we expect will be particularly helpful to study and understand the behavior of systems whose physics is unknown a priori, as well as to revisit a variety of physical phenomena under a new perspective.