This paper proposes new methods of computing 2D bifurcation diagrams for nonlinear time series using MultiLayer Perceptrons (MLPs), LSTM Fully Convolutional Networks (LSTM-FCN), Time Series Forests (TSFs) with entropy, Gini impurity, and K-Nearest Neighbors (KNNs) algorithm with Dynamic Time Warping (DTW). The proposed algorithms can precisely compute 2D bifurcation diagrams for oscillatory time-series (periodic or chaotic) obtained either as solutions of nonlinear systems of ordinary differential equations (ODEs) or measured and recorded when a mathematical model is not known. Illustrative computational examples include chaotic electric arc RLC circuits. The obtained results confirm usefulness of the proposed methods in a creation of 2D bifurcation diagrams — color images representing dynamics of nonlinear processes, circuits or systems.

本文提出了使用多层感知器 (MLP)、LSTM 全卷积网络 (LSTM-FCN)、具有熵的时间序列森林 (TSF)、基尼杂质和 K-最近邻 (KNN) 来计算非线性时间序列的 2D 分岔图的新方法) 算法与动态时间扭曲 (DTW)。所提出的算法可以精确计算振荡时间序列（周期性或混沌）的二维分岔图，这些分岔图可以作为常微分方程 (ODE) 的非线性系统的解获得，也可以在未知数学模型时进行测量和记录。说明性的计算示例包括混沌电弧 RLC 电路。获得的结果证实了所提出的方法在创建 2D 分叉图（表示非线性过程、电路或系统的动态的彩色图像）中的有用性。