A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors

R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied Dynamical Systems (2020) 705–723.

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Journal Article | Published | English
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Abstract
In this work we present a set-oriented path following method for the computation of relative global attractors of parameter-dependent dynamical systems. We start with an initial approximation of the relative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method. By using previously obtained approximations of the parameter-dependent relative global attractor we can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole subdivision procedure. We illustrate the feasibility of the set-oriented path following method by exploring the dynamics in low-dimensional models for shear flows during the transition to turbulence and of large-scale atmospheric regime changes .
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SIAM Journal on Applied Dynamical Systems
Page
705-723
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Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems. 2020:705-723. doi:10.1137/19m1247139
Gerlach, R., Ziessler, A., Eckhardt, B., & Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems, 705–723. https://doi.org/10.1137/19m1247139
@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}, DOI={10.1137/19m1247139}, journal={SIAM Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723} }
Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” SIAM Journal on Applied Dynamical Systems, 2020, 705–23. https://doi.org/10.1137/19m1247139.
R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,” SIAM Journal on Applied Dynamical Systems, pp. 705–723, 2020.
Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” SIAM Journal on Applied Dynamical Systems, 2020, pp. 705–23, doi:10.1137/19m1247139.

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