{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tor-a-toolbox-for-the-continuation-of-two","title":"Tor: a toolbox for the continuation of two-dimensional tori in autonomous systems and non-autonomous systems with periodic forcing","arxiv_id":"2012.13256","date":"2020-12-24","proceeding":null,"authors":["Mingwu Li"],"abstract":"We present a toolbox for the continuation of two-dimensional tori in autonomous dynamical systems and non-autonomous systems with periodic forcing. A torus is solved as the solution to a boundary-value problem. Truncated Fourier series and collocation methods are used to discretize the boundary-value problem. This toolbox is based on the continuation package COCO (https://sourceforge.net/projects/cocotools/). A few examples are included to demonstrate the functionality of this toolbox.","url_abs":"https://arxiv.org/abs/2012.13256v2","url_pdf":"https://arxiv.org/pdf/2012.13256v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"tor-a-toolbox-for-the-continuation-of-two","repo_url":"https://github.com/limw0601/torus_collocation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"tor-a-toolbox-for-the-continuation-of-two","repo_url":"https://github.com/mingwu-li/torus_collocation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}