This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the Hodgkin-Huxley formalism is considered. Single time series of one of its variables is shown to be enough to train a neural network that can operate as a discrete time dynamical system with one control parameter. The neural network system is created in two steps. First, the delay-coordinate embedding vectors are constructed form the original time series and their dimension is reduced with by means of a variational autoencoder to obtain the recovered state-space vectors. It is shown that an appropriate reduced dimension can be determined by analyzing the autoencoder training process. Second, pairs of the recovered state-space vectors at consecutive time steps supplied with a constant value playing the role of a control parameter are used to train another neural network to make it operate as a recurrent map. The regimes of thus created neural network system observed when its control parameter is varied are in very good accordance with those of the original system, though they were not explicitly presented during training.

翻译：本文研究利用单标量时间序列重构具有神经形态行为的动力学系统族。考虑基于Hodgkin-Huxley形式建立的生理神经元模型。研究表明，仅需使用其某一变量的单时间序列，即可训练出能作为单控制参数离散时间动力学系统运行的神经网络。该神经网络系统通过两个步骤构建：首先，从原始时间序列构建延迟坐标嵌入向量，并利用变分自编码器进行降维以获得重构状态空间向量。通过分析自编码器训练过程可确定合适的降维维度。其次，将具有控制参数功能的常数值与连续时间步上的重构状态空间向量对相结合，用于训练另一神经网络，使其作为递归映射运行。当控制参数变化时，该神经网络系统呈现的动力学状态与原始系统高度吻合，尽管这些状态在训练过程中并未显式呈现。