期刊
IEEE CONTROL SYSTEMS LETTERS
卷 7, 期 -, 页码 1566-1571出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LCSYS.2023.3275169
关键词
Windings; Jacobian matrices; Oscillators; Frequency synchronization; Synchronization; Kernel; Dynamical systems; Convergence; stability analysis; sufficient conditions; network systems; nonlinear network analysis; oscillators
This letter studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators using two recent concepts, namely appropriately-defined subsets of the $n$-torus called winding cells and the semicontractivity of the model. The letter establishes the local semicontractivity of the Kuramoto-Sakaguchi model and characterizes the multistability of the model by proving the at most uniqueness of synchronous states within convex phase-cohesive subsets of winding cells. The sufficient conditions and estimates provided in this work are less conservative and more explicit than previous studies.
This letter studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets of the $n$ -torus called winding cells. Second, we analyze the semicontractivity of the model, i.e., the property that the distance between trajectories decreases when measured according to a seminorm. This letter establishes the local semicontractivity of the Kuramoto-Sakaguchi model, which is equivalent to the local contractivity for the reduced model. The reduced model is defined modulo the rotational symmetry. The domains where the system is semicontracting are convex phase-cohesive subsets of winding cells. Our sufficient conditions and estimates of the semicontracting domains are less conservative and more explicit than in previous works. Based on semicontraction on phase-cohesive subsets, we establish the at most uniqueness of synchronous states within these domains, thereby characterizing the multistability of this model.
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