{"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/empirical-fixed-point-bifurcation-analysis","title":"Empirical fixed point bifurcation analysis","arxiv_id":"1807.01486","date":"2018-07-04","proceeding":null,"authors":["Gergo Bohner","Maneesh Sahani"],"abstract":"In a common experimental setting, the behaviour of a noisy dynamical system\nis monitored in response to manipulations of one or more control parameters.\nHere, we introduce a structured model to describe parametric changes in\nqualitative system behaviour via stochastic bifurcation analysis. In\nparticular, we describe an extension of Gaussian Process models of transition\nmaps, in which the learned map is directly parametrized by its fixed points and\nassociated local linearisations. We show that the system recovers the behaviour\nof a well-studied one dimensional system from little data, then learn the\nbehaviour of a more realistic two dimensional process of mutually inhibiting\nneural populations.","url_abs":"http://arxiv.org/abs/1807.01486v1","url_pdf":"http://arxiv.org/pdf/1807.01486v1.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":"abstracts"},"code_links":[{"paper_slug":"empirical-fixed-point-bifurcation-analysis","repo_url":"https://github.com/gbohner/thesis-code-chapter4-fpgp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.01486","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}