The numerical computation of unstable manifolds for infinite dimensional dynamical systems by embedding techniques

• Main Authors: Ziessler, Adrian, Dellnitz, Michael, Gerlach, Raphael
• Format: Journal Article
• Language: English
• Published: 28-08-2018
• Subjects: Mathematics - Dynamical Systems; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.1808.08787

In this work we extend the novel framework developed by Dellnitz, Hessel-von
Molo and Ziessler to the computation of finite dimensional unstable manifolds
of infinite dimensional dynamical systems. To this end, we adapt a set-oriented
continuation technique developed by Dellnitz and Hohmann for the computation of
such objects of finite dimensional systems with the results obtained in the
work of Dellnitz, Hessel-von Molo and Ziessler. We show how to implement this
approach for the analysis of partial differential equations and illustrate its
feasibility by computing unstable manifolds of the one-dimensional
Kuramoto-Sivashinsky equation as well as for the Mackey-Glass delay
differential equation.