The numerical computation of unstable manifolds for infinite dimensional dynamical systems by embedding techniques
Dynamical Systems
2019-09-24 v2 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.1808.08787,
title = {The numerical computation of unstable manifolds for infinite dimensional dynamical systems by embedding techniques},
author = {Adrian Ziessler and Michael Dellnitz and Raphael Gerlach},
journal= {arXiv preprint arXiv:1808.08787},
year = {2019}
}