A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine-Learning applications. Here, we describe several possible setups, which allow emulating multilayer (deep) feed-forward networks as well as recurrent networks of coupled discrete maps with arbitrary adjacency matrix by a single system with delayed feedback. While the network’s size can be arbitrary, the generating delay system can have a low number of variables, including a scalar case.

中文翻译：

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使用单个延迟微分方程模拟复杂网络

具有延时反馈的单个动态系统可以模拟网络。延迟系统的这种特性使它们成为机器学习应用程序中非常有用的工具。在这里，我们描述了几种可能的设置，它们允许通过具有延迟反馈的单个系统模拟多层（深度）前馈网络以及具有任意邻接矩阵的耦合离散映射的循环网络。虽然网络的大小可以是任意的，但生成延迟系统可以具有少量变量，包括标量情况。