Unveiling synchronization transitions in networks of coupled oscillators through persistent homology of local structures

Synchronization phenomenon characterize the collective behavior of complex systems. In recent years, data-driven approaches have become relevant because they can identify and quantify synchronized activity. Here, we study networks of mutually coupled Kuramoto phase oscillators adopting the normalized persistent entropy, NPE, based on persistent homology, as a synchronization quantifier, focusing our analysis on zero-dimensional homology groups of closed and open triads. We show that, as the coupling intensity increases, the NPE identifies transitions from incoherent to synchronized states in networks with different structural connectivity. We also use the NPE to analyze experimental data of mutually coupled electronic oscillators with Rössler-type dynamics, and identify transitions toward synchronization as the coupling intensity increases. Our results show that the NPE is a practical tool to quantitatively identify changes in the dynamics of networks of coupled oscillators.