On the computation of attractors for delay differential equations

TL;DR

This paper introduces a new method for computing finite-dimensional invariant sets in infinite-dimensional dynamical systems, specifically applied to delay differential equations, demonstrating its practical effectiveness.

Contribution

It extends classical subdivision techniques to infinite-dimensional systems using embedding results, enabling the analysis of delay differential equations.

Findings

Successfully computed invariant sets for three delay differential equations

Extended subdivision techniques to infinite-dimensional systems

Demonstrated feasibility through practical implementation

Abstract

In this work we present a novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems. It extends a classical subdivision technique [Dellnitz/Hohmann 1997] for the computation of such objects of finite dimensional systems to the infinite dimensional case by utilizing results on embedding techniques for infinite dimensional systems. We show how to implement this approach for the analysis of delay differential equations and illustrate the feasibility of our implementation by computing invariant sets for three different delay differential equations.