Time series classification and creation of 2D bifurcation diagrams in nonlinear dynamical systems using supervised machine learning methods

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.