{"_id":"16710","title":"A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors","department":[{"_id":"101"}],"publication_identifier":{"issn":["1536-0040"]},"date_created":"2020-04-16T14:05:41Z","user_id":"32655","citation":{"bibtex":"@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}, DOI={<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>}, journal={SIAM Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723} }","ama":"Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal on Applied Dynamical Systems</i>. Published online 2020:705-723. doi:<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>","mla":"Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, pp. 705–23, doi:<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>.","ieee":"R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,” <i>SIAM Journal on Applied Dynamical Systems</i>, pp. 705–723, 2020, doi: <a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>.","chicago":"Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, 705–23. <a href=\"https://doi.org/10.1137/19m1247139\">https://doi.org/10.1137/19m1247139</a>.","short":"R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied Dynamical Systems (2020) 705–723.","apa":"Gerlach, R., Ziessler, A., Eckhardt, B., &#38; Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal on Applied Dynamical Systems</i>, 705–723. <a href=\"https://doi.org/10.1137/19m1247139\">https://doi.org/10.1137/19m1247139</a>"},"year":"2020","status":"public","abstract":[{"lang":"eng","text":"In this work we present a set-oriented path following method for the computation of relative global\r\nattractors of parameter-dependent dynamical systems. We start with an initial approximation of the\r\nrelative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.\r\nBy using previously obtained approximations of the parameter-dependent relative global attractor\r\nwe can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole\r\nsubdivision procedure. We illustrate the feasibility of the set-oriented path following method by\r\nexploring the dynamics in low-dimensional models for shear flows during the transition to turbulence\r\nand of large-scale atmospheric regime changes .\r\n"}],"author":[{"full_name":"Gerlach, Raphael","last_name":"Gerlach","id":"32655","first_name":"Raphael"},{"first_name":"Adrian","last_name":"Ziessler","full_name":"Ziessler, Adrian"},{"full_name":"Eckhardt, Bruno","last_name":"Eckhardt","first_name":"Bruno"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"oa":"1","doi":"10.1137/19m1247139","date_updated":"2022-06-21T09:18:46Z","type":"journal_article","publication":"SIAM Journal on Applied Dynamical Systems","page":"705-723","main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/19M1247139","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published"}