This article is concerned about the synchronization problem of the bidirectionally coupled Kuramoto model. In this model, each oscillator only interacts with the oscillators with adjacent labeling numbers. Namely, the oscillator ${\theta }_i$ only interacts with ${\theta }_{i+1}$ and ${\theta }_{i-1}$. In real applications, this is a typical setting of concatenation connection. We first prove the global convergence of frequency synchronization for the identical oscillators. Also, we present two results of phase synchronization for the identical case in relatively wide initial configuration regimes. In the case that the coupling strength is sufficiently large (equivalent to the difference of the natural frequencies is sufficiently small), we show that for non-identical oscillators within a suitable initial configuration regime, the bidirectionally coupled Kuramoto model achieves a frequency synchronization. The supportive numerical simulations are presented as well.

本文关注双向耦合仓本模型的同步问题。在此模型中，每个振荡器仅与带有相邻标记编号的振荡器相互作用。即振荡器${\theta }_{\mathrm{一世}}$ 只与 ${\theta }_{\mathrm{一世}+\mathrm{1个}}$ 和 ${\theta }_{\mathrm{一世}-\mathrm{1个}}$。在实际应用中，这是串联连接的典型设置。我们首先证明相同振荡器的频率同步的全局收敛性。同样，我们给出了在相对较宽的初始配置方案中相同情况下相位同步的两个结果。在耦合强度足够大的情况下（等效于固有频率的差足够小），我们表明，对于合适的初始配置范围内的不相同的振荡器，双向耦合的仓本模型实现了频率同步。还提供了支持性的数值模拟。