标题： 噪声驱动的行波脉冲同步 显示英文标题

标题： Synchronization by noise for traveling pulses

摘要： 我们考虑通过噪声实现同步的随机偏微分方程，这些方程支持行波脉冲解，例如FitzHugh-Nagumo方程。 我们证明，任何两个从不同位置开始但由同一乘性噪声实现驱动的脉冲类似解，在时间尺度$\sigma^{-2} \ll t \ll \exp(\sigma^{-2})$上以概率收敛彼此，其中$\sigma$是噪声幅度。 假设噪声是高斯的，时间上是白噪声，空间上是色噪声且周期性的，并且仅在最低傅里叶模式中非退化。 证明使用了相位约简方法，该方法允许仅用其位置来描述随机脉冲的动力学。 位置被证明会同步，基于现有结果，并且相位约简的有效性使我们能够将同步转移回完整解。 显示英文摘要

摘要： We consider synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions but are forced by the same realization of a multiplicative noise, converge to each other in probability on a time scale $\sigma^{-2} \ll t \ll \exp(\sigma^{-2})$, where $\sigma$ is the noise amplitude. The noise is assumed to be Gaussian, white in time, colored and periodic in space, and non-degenerate only in the lowest Fourier mode. The proof uses the method of phase reduction, which allows one to describe the dynamics of the stochastic pulse only in terms of its position. The position is shown to synchronize building upon existing results, and the validity of the phase reduction allows us to transfer the synchronization back to the full solution.