Machine Learning of Nonlinear Dynamical Systems with Control Parameters Using Feedforward Neural Networks

TL;DR

This paper shows that simple feedforward neural networks can effectively reproduce bifurcation diagrams of nonlinear dynamical systems, such as the logistics map and coupled Stuart-Landau equations, demonstrating their potential in modeling complex dynamics.

Contribution

It introduces the use of feedforward neural networks for reproducing bifurcation diagrams, offering a simpler alternative to echo state networks for nonlinear dynamical systems.

Findings

Feedforward neural networks can reproduce bifurcation diagrams.

Successfully modeled logistics map bifurcations.

Captured synchronization transitions in coupled Stuart-Landau systems.

Abstract

Several authors have reported that the echo state network reproduces bifurcation diagrams of some nonlinear differential equations using the data for a few control parameters. We demonstrate that a simpler feedforward neural network can also reproduce the bifurcation diagram of the logistics map and synchronization transition in globally coupled Stuart-Landau equations.