相位同步中耦合与公共噪声之间的相互作用：全局分析与局部稳定性表征之间的不一致
Interplay between couplings and common noise in phase synchronization: disagreement between global analysis and local stability characterization
摘要：
我们考虑两个耦合的相位振荡器中存在的比例（“共同”）和独立的白噪声。利用Fokker-Planck方程研究了系统的全局同步性质。当“有效耦合”比一般噪声大时，前者有利于同步，后者阻碍同步。相反，当耦合是小的比例噪声相比，我们发现，后者诱导同步，最佳的时候，他们的强度是大的，在n：m同步比。此外，在这种情况下，小的耦合值对于同步更好。最后，我们表明，同步，这是一个全球性的，必须不通过本地稳定性，如李雅普诺夫指数的研究。
英文摘要：
We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the "effective coupling" is big compared to the common noises, the former favors and the latter hinder synchronization. On the contrary, when the coupling is small compared to the proportional noises, we find that the latter induce synchronization, optimally when their intensities are big and in the n:m synchronization ratio. Furthermore, in such case a small value of the coupling is better for synchronization. Finally, we show that synchronization, which is a global property, must not be studied via local stability such as with Lyapunov exponents.
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