论文标题
与内存有关的噪声引起的共振和非马尔科维亚系统的扩散
Memory-dependent noise-induced resonance and diffusion in non-markovian systems
论文作者
论文摘要
我们研究了非本地记忆的随机过程，并获得了描述非马克维亚系统的Mori-Zwanzig方程的新解。我们根据振幅$ν$和$μ_0$的本地和非本地记忆分析系统动力学，并注意（$ν$，$μ_0$）的线 - 飞机将区域与渐近和非平稳行为分开。我们获得了此类边界的一般方程式，并考虑了非本地记忆函数的三个示例。我们表明，存在两种类型的边界，具有根本不同的系统动力学。在第一种类型的边界上，随着记忆的扩散发生，而在第二种类型的边界线上，可以观察到噪声引起的共振现象。在所考虑的系统中，噪声引起的共振的一个独特特征是，它发生在没有外部正常周期力的情况下。它发生在噪声频谱中存在频率的原因，这些频率接近系统的自频。我们还分析了该过程的差异，并比较了其对渐近平稳性和非平稳性区域的行为，以及它们之间的扩散和噪声诱导的谐振边界。
We study the random processes with non-local memory and obtain new solutions of the Mori-Zwanzig equation describing non-markovian systems. We analyze the system dynamics depending on the amplitudes $ν$ and $μ_0$ of the local and non-local memory and pay attention to the line in the ($ν$, $μ_0$)-plane separating the regions with asymptotically stationary and non-stationary behavior. We obtain general equations for such boundaries and consider them for three examples of the non-local memory functions. We show that there exist two types of the boundaries with fundamentally different system dynamics. On the boundaries of the first type, the diffusion with memory takes place, whereas on borderlines of the second type, the phenomenon of noise-induced resonance can be observed. A distinctive feature of noise-induced resonance in the systems under consideration is that it occurs in the absence of an external regular periodic force. It takes place due to the presence of frequencies in the noise spectrum, which are close to the self-frequency of the system. We analyze also the variance of the process and compare its behavior for regions of asymptotic stationarity and non-stationarity, as well as for diffusive and noise-induced-resonance borderlines between them.
