Executive Summary : | The heterogeneous structure of complex networks significantly influences the synchrony or onset of epidemics, with hubs being major players. This study investigates dynamical networks with heterogeneity in node dynamics or topology from the perspective of extreme events, which are rare but recurring and significantly large deviations from the original dynamics. The research focuses on the role of hubs, repulsive interaction, and parameter mismatch in node dynamics in the formation of extreme events using techniques such as second-order phase oscillators, Liénard system, FitzHugh-Nagumo, or Hindmarsh-Rose neuronal systems. The study aims to control the devastating effects of extreme events in a dynamical network using suitable techniques. The dynamic origin of extreme events (EEs) in complex networks is not well explored, but the study addresses questions about the role of hubs, population responses to heterogeneity, mechanism behind events, topological heterogeneity causing EEs, and controlling the devastating effect of EEs. A data-driven approach is used for predicting extreme events (EEs) in manmade or natural systems, as early-warning detection of EEs is challenging due to the lack of suitable mathematical models or low real data. The study designs suitable deep or machine learning models for EEs in advance and uses them on real data from climate or neuron data connected with neuronal disease. |