Characterizing long-term cosmic ray time series with geometric network curvature metrics

Abstract

This study investigates the relationship between geometry and nonlinear dynamics in time series of cosmic ray counts recorded at neutron monitors at ground stations. Using advanced geometric and topological analysis techniques, we construct complex networks from the time series and calculate curvature measures such as Ollivier-Ricci curvature, Forman-Ricci curvature, and Ricci flow for each series. The analysis reveals significant correlations between these curvature metrics and key parameters such as geomagnetic cutoff rigidity and detector latitude. In particular, Forman-Ricci curvature exhibits a robust negative correlation with cutoff rigidity (Pearson $r=-0.85$, Spearman $\rho =-0.86$, $p$-value $<10^{-5}$), while Ricci flow also shows a strong and highly significant inverse relationship with cutoff rigidity (Pearson $r=-0.92$, Spearman $\rho =-0.89$, $p$-value $<10^{-7}$). These results suggest that the geometrical structure of the networks, influenced by geomagnetic conditions, plays a crucial role in the variability, complexity, and fractality of cosmic ray time series. Furthermore, the study underscores the importance of considering network topology and curvature metrics in the analysis of cosmic ray data, offering new perspectives for understanding space weather phenomena and improving predictive models. This integrative approach not only advances our knowledge of cosmic ray dynamics, but also has important implications for mitigating risks associated with space weather conditions on Earth.