Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany.
Institute of Physics and Material Sciences, Campus Limpertsberg, Université du Luxembourg 162 A, Avenue de la Faïencerie, Luxembourg.
Phys Rev Lett. 2023 May 5;130(18):187201. doi: 10.1103/PhysRevLett.130.187201.
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of complex locked states for coupling strengths K below the transition K^{(pl)} to classical phase locking. Stable complex locked states indicate a locked subpopulation of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that subpopulation. We uncover a second transition at K^{'}<K^{(pl)} below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths.
我们提出了有限大小的 Kuramoto 模型，从实变量解析延拓到复变量，并分析了其集体动力学。对于强耦合，同步通过锁定状态出现，这些锁定状态构成了吸引子，就像实变量系统一样。然而，对于耦合强度 K 低于经典相位锁定的转变 K^{(pl)}以下的情况，同步仍然以复锁定状态的形式存在。稳定的复锁定状态表明在实变量模型中存在一个零平均频率的锁定子群体，其虚部有助于确定哪个单元构成了该子群体。我们发现了第二个转变，在 K^{'}<K^{(pl)}以下，复锁定状态变得线性不稳定，但对于任意小的耦合强度仍然存在。
