  In this work, we analyze the Kuramoto model (KM) with inertia on a convergent
family of graphs. It is assumed that the intrinsic frequencies of the
individual oscillators are sampled from a probability distribution. In
addition, a given graph, which may also be random, assigns network
connectivity. As in the original KM, in the model with inertia, the weak
coupling regime features mixing, the state of the network when the phases (but
not velocities) of all oscillators are distributed uniformly around the unit
circle. We study patterns, which emerge when mixing loses stability under the
variation of the strength of coupling. We identify a pitchfork (PF) and an
Andronov-Hopf (AH) bifurcations in the model with multimodal intrinsic
frequency distributions. To this effect, we use a combination of the linear
stability analysis and Penrose diagrams, a geometric technique for studying
stability of mixing. We show that the type of a bifurcation and a nascent
spatiotemporal pattern depend on the interplay of the qualitative properties of
the intrinsic frequency distribution and network connectivity.
