Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it is found that the stability maps for the dimensionless equations show a high level of symmetry. The size of the attraction basins is numerically investigated. These sizes are changing periodically over several orders of magnitude as the parameters of the model are varied. Simple heuristic arguments are formulated to understand the changes in the attraction basin sizes and to predict the most probable states when the system is randomly initialized.

在具有时延最近邻居的相同仓本振荡器环中研究了相邻振荡器之间具有恒定相移的锁相状态。推导了这些状态的线性稳定性，发现无因次方程的稳定性图显示出很高的对称性。对吸引盆的大小进行了数值研究。随着模型参数的变化，这些大小会在几个数量级上周期性变化。制定了简单的启发式论据，以了解吸引盆大小的变化并预测系统随机初始化时最可能的状态。