We study the asymptotic complete entrainment of Kuramoto oscillators with inertia on symmetric and connected network. We provide several sufficient conditions for the asymptotic complete entrainment in terms of initial phase-frequency configurations, strengths of inertia and coupling, and natural frequency distributions. For this purpose, we reinterpret the Kuramoto oscillators with inertia as a second-order gradient-like flow, and adopt analytical methods based on several Lyapunov functions to apply the convergence estimate studied by Haraux and Jendoubi . Our approach does not require any spectral information of the graph associated with the given network structure.
Bibliographical noteFunding Information:
Y.-P. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2012R1A6A3A03039496 ). Z. Li was supported by 973 Program ( 2012CB215201 ) and KRF-2009-0093137 ( Korea Research Foundation ). S.-Y. Ha was partially supported by KRF-2011-0015388 ( Korea Research Foundation ). X. Xue was supported by NSF of China grant 11271099 .
All Science Journal Classification (ASJC) codes
- Applied Mathematics