Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow |
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Authors: | Young-Pil Choi Zhuchun Li Seung-Yeal Ha Xiaoping Xue Seok-Bae Yun |
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Institution: | 1. Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom;2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;3. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea;4. Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea |
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Abstract: | 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 21]. Our approach does not require any spectral information of the graph associated with the given network structure. |
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Keywords: | Kuramoto oscillators Inertia Network Complete entrainment Gradient-like flow |
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