Computing coherent sets using the Fokker-Planck equation

Andreas  Denner; Oliver Junge; Daniel  Matthes

doi:10.3934/jcd.2016008

Article Contents

2016, Volume 3, Issue 2: 163-177. Doi: 10.3934/jcd.2016008

This issue Previous Article Towards tensor-based methods for the numerical approximation of the Perron--Frobenius and Koopman operator Next Article Asymptotic invariance and the discretisation of nonautonomous forward attracting sets

Computing coherent sets using the Fokker-Planck equation

1.
Center for Mathematics, Technische Universität München, 85747 Garching bei München

Received: December 2015

Revised: October 2016

Published: June 2016

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Abstract

We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a discretized Fokker-Planck equation. For numerical implementation, we employ spectral collocation methods and an exponential time differentiation scheme. We experimentally compare our approach with the more classical method by Ulam that is based on discretization of the transfer operator of the unperturbed flow.

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Mathematics Subject Classification: Primary: 37M25; Secondary: 37N10.

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