Classification and Spatiotemporal Correlation of Dominant Fluctuations in Complex Dynamical Systems

The behavior of many complex systems, from nanostructured materials to animal colonies, is governed by local transitions that, while involving a restricted number of interacting units, may generate collective cascade phenomena. Tracking such local events and understanding how they emerge and propagate throughout these systems represent often a challenge. Common strategies monitor specific parameters, tailored ad hoc to describe certain systems, over time. However, such approaches typically require prior knowledge of the underpinning physics and are poorly transferable to different systems. Here we present LEAP, a general, transferable, agnostic analysis approach that can reveal precious information on the physics of a variety of complex dynamical systems simply starting from the trajectory of their constitutive units. Built on a bivariate combination of two abstract descriptors, LENS and {\tau}SOAP, the LEAP analysis allows (i) detecting the emergence of local fluctuations in simulation or experimentally-acquired trajectories of any type of multicomponent system, (ii) classifying fluctuations into categories, and (iii) correlating them in space and time. We demonstrate how LEAP, just building on the abstract concepts of local fluctuations and their spatiotemporal correlation, efficiently reveals precious insights on the emergence and propagation of local and collective phenomena in a variety of complex dynamical systems ranging from the atomic- to the microscopic-scale. Given its abstract character, we expect that LEAP will offer an important tool to understand and predict the behavior of systems whose physics is unknown a priori, as well as to revisit a variety of known complex physical phenomena under a new perspective.