{"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/the-van-der-pol-equation","title":"The Van der Pol Equation","arxiv_id":"0803.1658","date":"2008-03-11","proceeding":null,"authors":["Marios Tsatsos"],"abstract":"In this work, we present the basic theoretical efforts that are known in order to deal with non-trivial solutions of the Van der Pol oscillator, such as theory of average, successive approximations and symbolic dynamics. We also construct a set of diagrams (bifurcation, 2D and 3D Fourier power spectra) and maps, based on numerical investigations, corresponding to the expected theoretical results. Furthermore we examine closely the existence of chaotic attractors, both theoretically (with symbolic dynamics) and numerically (period doubling cascades). We show how we constructed sound files, based on the Fourier spectra, each one corresponding to a periodic, an almost periodic and a chaotic solution, as one of the parameters of the system alters.","url_abs":"http://arxiv.org/abs/0803.1658v1","url_pdf":"http://arxiv.org/pdf/0803.1658v1.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":"the-van-der-pol-equation","repo_url":"https://github.com/goolulusaurs/ChaoticAttractors","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-van-der-pol-equation","repo_url":"https://github.com/yangyucheng000/werf158297","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","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}