Stability of Clusters in the Second-Order Kuramoto Model on Random Graphs

The Kuramoto model of coupled phase oscillators with inertia on Erdos-Renyi graphs is analyzed in this work. For a system intrinsic frequencies sampled from bimodal distribution we identify variety two cluster patterns and study their stability. To end, decompose the description dynamics into systems: one governing (macro) centers mass clusters second (micro) individual inside each cluster. former low-dimensional ODE whereas latter Vlasov PDEs. Stability depends stability group motion coherence group. We show that loss leads to two-cluster state formation chimera states. analysis paper can be generalized cover states more than systems W-random graphs. Our results apply power grid fluctuating sources.