期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 17, 期 1, 页码 457-483出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1084390
关键词
asymptotic stability; phase difference; Kuramoto oscillators; time-varying couplings
资金
- National Natural Sciences Foundation of China [61673119]
- Key Program of the National Science Foundation of China [91630314]
- Laboratory of Mathematics for Nonlinear Science, Fudan University
- Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University
We study dynamics of phase differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In the case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable if there exists T > 0 such that the aggregation of the time-varying graphs across any time interval of length T has a spanning tree. We also consider the situation that the coupling coefficients may be negative and provide sufficient conditions for the asymptotic stability of the PD dynamics. Due to time variations, the PDs are asymptotic to time-varying patterns rather than constant values. Hence, the PD dynamics can be regarded as a generalization of the well-known phase-locking phenomena. We explicitly investigate several particular cases of time-varying graph structures, including asymptotically periodic PDs due to periodic coupling coefficients and intrinsic frequencies, small perturbations, and fast-switching near constant coupling and frequencies, which lead to PD dynamics close to a phase-locked one. Numerical examples are provided to illustrate the theoretical results.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据