Visual exploration of 2D autonomous dynamical systems

TL;DR

This paper introduces ASysViewer, an interactive visualization tool for 2D autonomous dynamical systems that improves understanding of vector fields by accurately depicting critical points and separatrices, overcoming limitations of traditional plots.

Contribution

The paper presents ASysViewer, a novel application utilizing line integral convolution and grid-based methods for enhanced visualization of dynamical systems, tailored for educational use.

Findings

Improved visualization of critical points and separatrices.

Enhanced understanding of vector field behavior.

Interactive exploration for educational purposes.

Abstract

In an introductory course on dynamical systems or Hamiltonian mechanics, vector field diagrams are a central tool to show a system's qualitative behaviour in a certain domain. Because of their low sampling rates and the involved issues of vector normalization, these plots give only a coarse insight and are unable to convey the vector field behaviour at locations with high variation, in particular in the neighborhood of critical points. Similarly, automatic generation of phase portraits based on traditional sampling cannot precisely capture separatrices or limit cylces. In this paper, we present ASysViewer, an application for the interactive visual exploration of two-dimensional autonomous dynamical systems using line integral convolution techniques for visualization, and grid-based techniques to extract critical points and separatrices. ASysViewer is addressed to undergraduate students during their first course in dynamical systems or Hamiltonian mechanics.