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arXiv · 1808.08787

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

Adrian Ziessler·Michael Dellnitz·Raphael Gerlach
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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.

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Adrian Ziessler, Michael Dellnitz, Raphael Gerlach. 2018-08-27. The numerical computation of unstable manifolds for infinite dimensional dynamical systems by embedding techniques. https://doi.org/10.1137/18m1204395

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