{"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/deficiency-of-chemical-reaction-networks-the","title":"Deficiency of chemical reaction networks: The effect of operations that preserve multistationarity and periodic orbits","arxiv_id":"2305.19410","date":"2023-05-30","proceeding":null,"authors":["Awildo Gutierrez","Elijah Leake","Caelyn Rivas-Sobie","Jordy Lopez Garcia","Anne Shiu"],"abstract":"We investigate six operations on chemical reaction networks, all of which have been proven to preserve important dynamical properties, namely, the capacity for nondegenerate multistationarity (multiple steady states) and periodic orbits. Both multistationarity and periodic orbits are properties that are known to be precluded when the deficiency (a nonnegative integer associated to a network) is zero. It is therefore natural to conjecture that the deficiency never decreases when any of the six aforementioned network operations are performed. We prove that this is indeed the case, and moreover, we characterize the numerical difference in deficiency after performing each network operation.","url_abs":"https://arxiv.org/abs/2305.19410v2","url_pdf":"https://arxiv.org/pdf/2305.19410v2.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":"deficiency-of-chemical-reaction-networks-the","repo_url":"https://github.com/caelynsobie/deficiency-calculator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}