Low-dimensional behavior of Kuramoto model with inertia in complex networks.
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.
1] Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany [2] Department of Physics, Humboldt University, 12489 Berlin, Germany.
Peng
P
Ji
Instituto de Física de São Carlos, Universidade de São Paulo, Av. Trabalhador São Carlense 400, Caixa Postal 369, CEP 13560-970, São Carlos, São Paulo, Brazil.
Thomas K D M
TK
Peron
Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos, São Paulo, Brazil.
Francisco A
FA
Rodrigues
1] Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany [2] Department of Physics, Humboldt University, 12489 Berlin, Germany [3] Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
Jürgen
J
Kurths