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Low-dimensional behavior of Kuramoto model with inertia in complex networks
Peng Ji1, Thomas K D M Peron2, Francisco A Rodrigues3
11] Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany [2] Department of Physics, Humboldt University, 12489 Berlin, Germany.
Abstract:
Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.
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