1 research outputs found
Stability of phase difference trajectories of networks of Kuramoto oscillators with time-varying couplings and intrinsic frequencies
We study dynamics of phase-differences (PDs) of coupled oscillators where
both the intrinsic frequencies and the couplings vary in time. In 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 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 generalisation 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.Comment: 33 pages; 3 figure